Watch them catch the horse and handle him. To me, it's a red flag if I go to look at a horse and they're working him under saddle (granted, I don't own a horse, and this only happened once when I actually got to go look at a horse, but still...). Too many people get "dead broke" horses who turn out to have been dead broke because they were so heavily doped on tranquilizers they were barely standing.
Lameness/colic issues, as mentioned - I didn't know much about the past of the gelding I owned for a while, but a very knowledgeable friend told me he'd had laminitis a year before I got him - he had wavy growth lines on his hoof wall. How well they're trained - said gelding was supposed to be fairly well trained; he wasn't. How he handles the farrier, vet, trailer, clippers, washrack, new situations, trail riding, crowds, etc. Is he safe for small children to be around (you might not be planning to have him around small children, but it's something to indicate his temperament, and you never know, the occasion might arise).
Don't fall in love with a pretty face. Some of the prettiest horses I've ever known were fruitcakes once you got to know them.
I don't mean to sound rude or condescending or anything (to be honest, it's 1 am, and I've no idea what I'm even still doing awake), but if you're asking us what questions to ask, it'd better not be a stallion - if you had the experience to handle a stallion, you'd know what to ask (I know what to ask, but I'm not sure I'd want to put up with the bother of having a stallion).
Um...pedigree. Is he registered? Write down his pedigree information and do some research. Take a camera along and get some conformation shots and some shots of him under saddle.
Of course, the most important question is one only you can answer: is this horse suited for you? Will he fulfill your requirements? Do you want something you can bop along on trails with, or a serious show competitor?
Right. I'm turning off my computer now and going to bed. Eighteen solid hours of consciousness is too much.