Can anybody tell me what to look for in garage sale bows, as in things to check for and how to spot problems. Will problems be obvious? Thanks!

Sometimes you can not see any problems.
I bought a garage sale bow in Colorado that looked just fine, one day I was shooting in the back yard and it came apart at the handle.  Then again I bought one in an Army surplus -15yrs ago- that still shoots good.

Take a srtinger along with you. IF the bow has a viable string, string it up, hold one tip in hand put other tip on ground, rock it back and forth and see if the string is centered.  Does the string line up with string grove below the tips if it has these. This will help with limb twist.   Look for cracks and splits along the edges of the limbs, look for discoloration in the glass on the limbs, any bubbles, delamiantions,  lots to look for but there are a lot of good bows out there that will last for years while other will fall apart on yea ....

Garage sale bows are a crap shoot.  I bought a shakespeare wonderbow for $.25  (25 cents) made a string fo it and shot a fox with it.  Turned out to be a real shooter.  I look at it this way.  If they are  cheap enough, buy it.  If it turns out to be a bad one, cut the limbs off and screw the handle to the outhouse door !!!

Jon,  I like your use of extra bow parts.  I use broken & exploded bows for knife handles usually nice wood...Jeff

Good point Jon, I guess I was not expecting to find anything that cheap, but for that little it is worth the chance, and thanks Tippit for pointing out the possibility of knife handles if the bow explodes. Duh, I guess some bow would be more than worth it just for the wood.