Ah...so many things. The main things I look for are:
1) Quality of the main materials - is the leather soft, is it strong or fragile? Is the leather dyed or just painted? Is the metal hardware finished evenly, without chipping?
2) Quality of the construction - No glue on the seams, even stitching, hardware attached securely, zipper works smoothly, etc.
3) Style of the bag - will it go out of style in 20 minutes, or is it a classic? Will the color go with everything, or is it funky enough to have very limited use? Any of these are OK, but they are considerations, especially if it's an expensive bag.
4) Design of the bag - is it balanced, or does it sag in the middle? Can it be opened comfortably or do you have to squeeze your hand in to get something out?