Can you be blinded by a 'dim' light? From what I can tell, if you pick a color near the extreme of the visible light spectrum, let's say red, and trace a path across the spectrum until you are outside of the visible range, at some point the red color will begin to darken and dim until it's invisible (ie. black), indicating that you are now outside the range.

If this is the case, does that mean that if you were to observe a powerful enough light source emitting solely that dim frequency, that it could be blinding to your eyes? By blinding, I don't think I mean literally blocking the rest of your vision, but more as in painful or overly-stimulating, the same way a bright white or bright blue light can affect a person's sight.
It is hard to imagine being blinded by a dim light, because usually when you increase the intensity of the light, the saturation of the color will increase, until it appears bright. In this special case though, the color is already fully saturated to begin with, so no matter how high you increased the intensity, it will always appear 'dim'. Is this right?
EDIT:
Comments have shown that the word I was searching for is dazzled, not blinded. There are some great answers here explaining the harmful effects of this type of light, and this is a legitimate interpretation of what I am looking for. The essence of the question, however, is to understand if a near-IR or near-UV light could have a dazzling effect on the observer's eyes. 
 A: Yes indeed, infrared light (the wavelengths beyond those of red light) can be very harmful to your eyes even though you don't see them. The same applies for ultraviolet light (the wavelengths beyond those of violet light). 
You can read more under the topic of laser eye safety. People that work with lasers need to use safety glasses if these lasers fall within certain categories. These include infrared and ultraviolet lasers.
A: Some corrections: The color does not darken in the sense that it is getting black, but the brightness diminishes. Every color is getting black if you put a neutral filter before which only reduces brightness.
You are right that there is no hard border of visibility in the IR range. The normal given range is 700 nm wavelength for red, but e.g. a diode pumping laser of 808 nm which is powerful enough to burn through paper in less of a second emits a very visible dark red. In a darkened room you can even see the light of a Nd-YAG laser with 1064 nm if you set the power high enough to cut steel plates.
But in all these cases the damage for eye and even skin is far too great before you are reaching intensity levels which could be dazzling. Even diffuse reflection is dangerous at these power levels.
A: 
By blinding, I don't think I mean literally blocking the rest of your vision, but more as in painful or overly-stimulating, the same way a bright white or bright blue light can affect a person's sight.

I'm not sure what you mean by literally blocking the rest of your vision, but an overly-stimulating light can be described as dazzling. If that's what you mean (as opposed to eye damage, which other answers extensively cover), then no, intense IR/UV will not dazzle you: you will still be able to see clearly with such an intense source in your FOV. That's how those privacy googles are made: the IR is strong enough to dazzle the cameras, but doesn't disrupt human vision.
A: To add to the other answers (and Flippiefanus's answer) that both invisible IR and UV light can permanently damage the eyes without any sensation of damage or injury being felt.
Invisible IR damage causes damage through thermal loading: the retina absorbs heat from incident light faster than its vascular network can draw the heat away. High power UV can do the same, but for shorter visible and UV wavelengths a second mechanism is photochemical toxicity - where photons of energy comparable to organic molecule bond energies beget chemical changes in the retina or even nuclear (in the biological sense) DNA changes with the attendant neoplasia risk - is a much more dangerous factor because it is damaging at far lower levels than are needed for thermal damage to happen. Basically, the retina can safely absorb of the order of five to ten milliwatts of light focussed to a spot of less than about $50{\rm \mu m}$ diameter, and laser and light safety standards aim to limit light entry to the eye of less than $1{\rm mW}$ at IR wavelengths where only thermal loading is a problem. Laser safety standards, in particular, IEC/ISO 60825, aim to limit power input to the eye at visible and UV wavelengths to only a few microwatts owing to the danger of photochemical damage.
Long term, chronic exposure to UV is even more of a problem. Cataracts arising from photochemical damage to proteins are the foremost cause of human blindness on the planet. Very long term, chronic exposure to low levels of UVB such as one encounters on normal, sunlit days, especially at lower, tropical latitudes or snowy environments, are an overlooked hazard. One should generally encourage children to wear sunglasses, conforming to a sound eye protection standard, as the eye's lens is particularly transparent to UV under the age of 20.
Lastly, there is even some evidence that high peak powered IR pulses can give rise to severe photochemical damage and that the laser safety standards are inadequate in the way they deal with it. See for example:
Glickman R. D., "Phototoxicity to the retina: mechanisms of damage", *Int. J. Toxicology". 2002 21, #6, 2002, pp473-490
Not being a biologist/ ophthalmologist, I am not fully qualified to read this paper. But it does sound thoroughly reasonable from a physicist's standpoint. On interaction with the complicated organic molecules in the eye, high peak power pulses yield much shorter wavelength light through nonlinear processes. Significant production of even UV can result, hence the risk of photochemical damage. The problem here is that the safety standards (including ISO60825) blithely assume that the thermal loading on the retina is the only problem. Therefore, they are too forgiving of pulsed lasers with small duty cycles: the standards will accept a level of laser power as intrinsically safe if its average power is small. As I have discussed, very low levels of UV can be a problem, and this is even more so when the light enters the eye as IR as it is then deeply penetrating. Conversion to shorter wavelengths can happen beneath the retina's layer of shielding melanin, so the retina is particularly vulnerable to this kind of exposure. 
Therefore, until the standards are updated to account for this factor, I have been assuming that IR light is a mixture of IR together with one tenth of its power at each of one half and one third of its nominal wavelength, and applying the safety standards both to the IR and the assumed second and third harmonic UV if I am called on. This is obviously highly conservative, especially if the IR light isn't pulsed, but until someone convinces me that the standards are taking these things into account, that's what I am going to do. 
A: The short-form question is, at the time of this answer, "Can you be blinded  by a 'dim' light?" with clarification that "blinded" means "dazzled" ("to lose clear vision especially from looking at bright light").  This answer addresses lights that appear dim due to intensity, not wavelength. 
Here is a simple exercise I use to demonstrate an affirmative answer.  You can try this on your own (at-home participation) if you'd like (safety notes at end). 
Start in a dark place, like a room or outdoor setting as dark as you can make it (ideally, with little moon).  Place one tea light or other small candle in the middle of a circle of people.  Instruct everyone to stare at the candle flame, cover one eye with their hand, and hold their hand there for 5-10 minutes.  
During that time you can tell a story (or listen to an interesting one) etc.  I like to pick one about the surprising amount of impact even something traditionally regarded as the least powerful in its category can have.  Think of how many candlepower even relatively "dim" lightbulbs have, and how even bright electric lights are completely dwarfed by daylight!  
At the end, blow out the candle and then instruct people to uncover their eye. There should be a noticeable difference between what can be seen with one eye and what can be seen with the other.  The dim light of the candle has caused vision impairment in the eye that was left uncovered. It's been dazzled. 
Safety considerations: This is not a permanent impairment and the effect should go away after a while (on the order of several minutes) as the eyes adjust to the ambient level of brightness.  Use all precautions that apply to situations with candles/open flames, and those which apply to bumbling around with impaired vision in your selected environment. 
A: In response to the edited question which went after the idea of being "dazzled" by the light, it would not work the way you would like.
We show the spectrum "darken" as we leave the visible region, because we are showing a roughly constant intensity of light from one side of the spectrum or the other.  When you start talking about making the light brighter, we have to be a bit more formal:

Graphs like the one above show the frequency response of our cones.  There's a few variants on the y-axis (some use a unit system where the blue is more sensitive), but it doesn't matter for this answer.
We can see that as we move past 700nm, into IR, the red light response goes down.  But it doesn't go to zero right away.  So if you had a very bright light just outside this region, it would stimulate the red cones in your eye.
But here's the trick: for all pain and dazzling responses, we rely on the signals that we receive from the rods and cones.  There are no pain neurons in the retina, so these are all the signals our brain gets (and obviously it has to become a signal to the brain before it could dazzle us).
So what we would see with your very bright IR light is an ultra-pure red -- bothersomely pure because it's so far away from the peak of the green cones.  But you would not see it as "dim," because by definition, you're stimulating the cones to cause the dazzling effect.  It would have to appear very bright, just like any other dazzling light.
Of course, the limit to this is when you get to the IR region where your sensitivity gets low enough that second order effects (like thermal heating) become important.  That's where the other answers pick up.  But below that point, the light would be dazzling because it's bright, or it would not be dazzling because it's dim.  You can't have dazzling and dim from a signal processing perspective.
A: Yes, and indeed this is a very important issue. And the real serious part is - unlike what you've said, it may not, and perhaps even will not, be "painful". And the reason for that is that the perception of any sort of discomfort or pain, "over-stimulation", etc. can only happen if the eye is actually stimulated by the radiation in question. And by definition, these rays do not stimulate the eye, so it cannot react with pain. And this kind of intensity is very often encountered with lasers, and it is a significant safety hazard. In particular, if the laser is intense but at a wavelength the eye does not readily perceive, it may notice little to no light, and feel little to no pain, so none of the usual defensive reflexes will be triggered (including the all-important pupil constriction response) ... until that damage has already been done, which is often rather quick.
Now of course, not all wavelengths will affect the eye in the same way, as the eye's materials, like anything else, are not necessarily transparent to or respond to all wavelengths in the same way. In particular, if the radiation frequency is sufficiently low, so the wavelength sufficiently long and thus far into the infrared, it will not be able to reach the retina, but can still reach the cornea (the part of the eye that is on the outside of the lens) and cause damage there, which may not be immediately apparent but puts one at risk for cataracts. Indeed this can also happen with intense diffuse sources of such longer-wave infrared light as well with prolonged viewing, e.g. "glassblower's cataracts", due to the emission of infrared radiation from the hot glass, which is vastly more intense than the radiation in the visible (the "red/yellow glow" you see, which is usually not bright enough to itself be harmful - that requires much higher temperatures like those on the Sun. This can be seen from a graph of the Planck curve at suitable temperature - usually about 1400 K - although of course glass is not a great blackbody radiator given its transmissivity in the visible, but nonetheless it is especially opaque to far or long wave infrared (hence why that thermal infrared cameras need to be made with germanium lenses instead of glass lenses) and thus will be a better blackbody there.) but because of its long wavelength does not reach the retina, but instead the cornea, causing totally painless, YET HARMFUL, heating. A special infrared-blocking goggle is thus standard protective wear for this purpose, if one is going to glass-blow professionally and thus be exposed to this radiation on a long-term basis. (Lasers, due to their concentrated, monochromatic nature, will require different goggles - be warned and do NOT mix the two up, in EITHER direction, but ESPECIALLY not with lasers because their damage is instant, not gradual.)
In other words, YES you can be "blinded" (though not likely to be complete blindness, but get a "spot" in your macula and that can very well be effective blindness! And that's where you're most likely to get one because that's what you use to look at things!). And even worse, NO you might very well NOT feel pain until it's too late. And to answer your question about it "always appearing 'dim'" - yes, that's right - until it vanishes because it destroyed your retinal cells (for wavelengths that can penetrate the cornea and humours to reach the retina, that is) or at least stops getting "brighter" because your eye has been damaged just same but before the receptors gave off enough of a signal to tell your brain to perceive intense light. The radiation can't get bright enough to elicit a "bright" perception before your eye is damaged, often permanently, and often in the worst possible spot. The threshold for such wavelengths to elicit bright perception exceeds the threshold to destroy the receptors.
MAKE SURE TO PROTECT YOUR EYES with suitable goggles, ESPECIALLY with lasers - if you miss your goggles and you catch a beam in the eye that could be the end of your easy life and it's all the worse when those beams are invisible in every way (not even a visible spot on the wall, much less scattered light from air or suspended particulate)! And NEVER operate any remotely serious laser - that is, more than a laser pointer (which is ok so long as you DO NOT POINT IT IN your eyes) - without a good course in laser safety procedures.
