first, differenent price range used bikes looks for different things..
if you are planning to spend 50 - 100 bucks on a used bike...as long as it runs...its fine....
if u are looking into 1k used bikes...then there are more to look for
*frame tubing....dents, bent, dings, wear
*wheelset - true, no flat spot, smooth hubs, braking surface
* fork - level, condition (if its air, does it leak)
* brakes - good stopping power? (if hydro disc, leak?, etc)
there are many things to look for in a used bike....