Some good quick answers here. I just saw this years later and felt like taking a crack. :P
[radio wave part]
There are so many sources where they could reflect and cancel out or annoy each other..
Yes, and that's exactly what they do. They step on each other's toes and, in general, obey the principle of superposition.
Shouldn't radio waves not work at all?
You know they do. (It's a useful guide, sometimes.) So, the question is, why do they still superimpose in a "coherent" way? The following will use a radio as an example.
Ideally, an antenna is going to get hit harder with the more direct path from the source, than from indirect paths that bounced around the neighboring geometry. Depending on the frequencies you are tuning to and the time-of-flight delay for these indirect paths, this might not be a problem. Radio waves from other sources could interfere, as well. In the end, you get a stronger signal, superimposed with maybe somewhat-off and not as strong signals, superimposed with some weaker random noise. (again, ideally)
At least, this is what things look like to the antenna. The antenna, being a transducer, changes the problem for us at this point. From the antenna on, we start dealing with current being driven through circuits, which has it's own noise contributions, but also it's own mechanisms for signal processing, that produce what you hear out of the radio.
Basically, all that complicated superposition wave stuff that you thought was happening actually is happening. It's just that it can be dealt with.
[color perception part]
Why doesn't that actually happen? Any time I look into a wall, I never see the wall "cancel out" of my perception.
Your eye has a lensing structure at the front, a water-like fluid in the middle, and a bio-transducer mechanism at the back. (I like to think of light in terms of rays/photon-paths when thinking about lenses.)
The lensing structure at the front acts as a a kind of filter. All the background stuff is targeted to miss the back of your eye, so only the photons following a particular path will hit on "that particular part of the back of your eye". (Note: maybe some degenerate paths here.) This corresponds to receiving some bunch of photons from a perceived ray in the world.
There are different kinds of transducers in the back of your eye and they have different spectral responses. The game here is then statistics on the kinds of photons received and the functioning of your transducers at that location. (See, for example, color blindness.) Regardless, you are biologically wired (from the brain to the eye) to figure out some light/color perception from this bunch of photons at that spot at the back of your eye. (And you have two eyes, see: binocular vision.)
So, again, all that complicated stuff is happening. In this case, it is you that has evolved to deal with it.