Is it bad for the bike to pedal backwards? Whenever I near yellow or red lights, I slow down and pedal backwards as I coast so that I can continue to get exercise while I wait for the light to turn green before I reach the intersection. (It's a mountain bike; it doesn't have a coaster brake.)
Is this bad? From what I've read, crank-arms are supposed to tighten themselves as you pedal, so does that mean pedaling backwards loosens it? 

(The only thing I can find when doing a web-search on this is about whether it's physically beneficial to pedal backwards on a recumbent bike, not about the effects on a bicycle.)

Note: Some people have mentioned that it's not exercise because of the low resistance, but that's like saying that a motor with no load doesn't burn any fuel or battery to turn. It may not be a hard exercise, but it's still movement. Moreover, there is another point to coasting toward the intersection in that coming to a complete stop at the light requires a lot of exertion to get back up to speed and it's very frustrating to feel rushed, trying to get across while cars wait. By coasting, I'm able to much more easily get through the intersection quickly once the light turns green.
There are a couple of things you should consider:

Your bike isn't going to care. You aren't going to loosen pedals or cranks spinning in reverse, because you're not applying any load, so there is no force in which to cause precession or fretting.

You are getting no benefit (health-wise) from doing so. It might be better not to even bother.