Check for any crash damage, esp frontal hits. Look for any bulging or paint flakes on the tubes just behind the head tube.
Ping the spokes to check for even tension.
Excessively worn cogs will show up as sharks-tooth shape.
Make sure the seatpost is not siezed into the frame.
On a used bike, look for the best quality frame and components you can. There is no excuse for bying a used bike which was crappy when it was new. Good bikes remain good even when old.