Why doesn't the light from galaxies appear stretched? Maybe it's my ignorance of astrophysics/cosmology, but I have been wondering this:
Why do galaxies not appear stretched when we observe them? Assuming a galaxy that we observe is 100,000 light years in diameter, and we are viewing at an angle that is almost sideways, but enough to see its shape, there would be a 100,000 year delay between what we see at the front of the galaxy versus the far end of the galaxy. So wouldn't it look all jumbled up instead of a perfect spiral?
At first, I thought that the Big Bang would explain this, because the light from that matter would have been there from the start, but that doesn't make sense when we consider that it took hundreds of thousands of years for the universe to clear up enough for photons to travel far in any direction without bouncing of of something. Also, if inflation theory is true, wouldn't that just reinforce the confusion about the delay in light, being that the universe expanded faster than light for an instant?
It's confusing, but if someone has an answer for this I'd appreciate the enlightenment.
 A: Galaxy rotation happens at a very slow rate (compared to the speed of light). Let's suppose you are observing a galaxy edge-on that the delay from the farthest point is $\Delta t = d/c$, where $d$ is the galaxy diameter. If we take the lag from one extreme point to the other as D:
$D = vt = \frac{v}{c}t$
(where $v$ is the rotational speed).
You can see that, to have an appreciable effect, your velocity must be a fraction of the speed of light.
The Milky Way rotates at a speed of $\sim10^2$ km/s, which is $\sim10^{3}$ times less than $c$. This means that your lag from one point to the opposite one of the galaxy is exceedingly small.
Of course, it is possible that for larger galaxies (see, e.g., Hercules A) you can have faster rotation, but you still need a coincidence of factors like distance, angle, and size of the galaxy, to appreciate a small difference in the lag. And this, as far as I know, has never been observed yet.
A: Galaxies would appear stretched along the line of sight, not jumbled.  Let's say a galaxy (specifically, the closest side of it) is ten million light years away and, as you proposed, is 100,000 light years across and we see it nearly edge on.  The front of the galaxy will appear to us as it did ten million years ago and the back of the galaxy as it did 10,100,000 years ago.  Thus, if the galaxy is moving towards us it will appear bigger than it actually is due to the delay between light from the front of the galaxy and the rear of the galaxy reaching us.  If the galaxy is moving away from us, it will appear smaller than it actually is (compressed along the line of sight).
As far as the effects of this time delay on viewing the rotation of the galaxy, the length of the cosmic year (the length of time it takes for the sun to travel around the center of the Milky Way) is 225 to 250 million years.  So, as many other people have already pointed out, the rotation period of a galaxy is small compared to the time it takes for light to travel across the galaxy and there is no jumbling effect.
A: I think the very short answer is:
galaxies are very small, indeed tiny, compared to how far away they are, and secondly, compared to the size of the universe.
The answer to the spirit of your question, is that simple!  "Galaxies are tiny."
You're used to hearing "galaxies are 100,000 light years across!" but that's a piffle compared to either the size of the universe, or, how far away they are from us.
Note that in your question it's somewhat unclear if you mean the seeming paradox due to redshift (in which case the answer is: galaxies are incredibly small compared to the universe), or, if you mean a seeming paradox something to do with spinning/perspective (in which case the answer is: galaxies are incredibly small compared to our distance to them).
Note that with galaxies very close to us, as I understand it, it is indeed commonplace for Astronomers to be able to measure different qualities on one side or the other (again: your question is somewhat unclear "which" seeming-paradox you mean, but as I say, indeed for "nearby" (lol) galaxies, in fact yes, it's an everyday thing to measure "bending" and other stuffs).

Note: piffle is a new SI unit with the definition "quite a many to damned many orders of magnitude".
A: I suspect that the nice rotational formations of galaxies we see come from galaxies that are oriented in parallel with our solar plane so that the light  arrives almost synchronously. 
Considering we are talking of gravitational forces the "almost" could cover a large window, the distortions not being too great to lose track of the shape. A galaxy whose plane is perpendicular to the solar plane would not show the rotational curves anyway, due to superposition. I do not know whether the shape of the infrared spectrum could be characteristic, i.e. gives some hint that the rotational curves exist.
