My partner plays cello and I play upright bass. I'd ask to hear every string played up and down the fingerboard. Listen for buzzes. Look for any separation at the seams between the top, sides and back. Also between the fingerboard and neck.
Mostly though, just see what it sounds like. I'd always say it's worth taking an instrument to a luthier once it's been played for a while to iron out anything you're not happy with. Minute things like sound post and bridge positioning can make a massive difference to the sound.
Also the bow. Try to see how much hair has broken and whether it'll be in need of a re-hair soon. That can cost a bit, but not a lot. Could be a good bargaining chip if you're looking for a reduction.