Try everything you can on the prospective lathe. If you don't know how have the person show you. If he or she doesn't know how to make it go, do your best to try most of the spindle speeds, the longitudinal feed and cross feed. Do this with several feed rate changes at the gearbox. This exposes shifting or gearbox problems. Try it in reverse also. Most lathes will make more gearbox noise in spindle reverse but this is normal.
Lathes that have seen heavy use will have the paint worn off up in the headstock and chuck area with the paint wear leading down into the chip pan. Check the backlash of the cross feed (X axis)screw. This is when you turn the handle a turn or two turns in one direction then stop, then turn it in the opposite direction and note how many thousandths on the dial it takes before the apron moves in the second direction. A nice tight machine will be .010 but anything up to .025 is not bad. Run the apron the full length of the machine note any clunks of notches. Up near the chuck is where the apron gets used most. Note if it gets tighter when you run it all the way to the tailstock end of the machine. This can indicate wear or just lack of lubrication to the ways. It can also mean there is accumulated dirt so if you feel some tightening look for a logical reason.
Everything should work smoothly on a good industrial grade machine. All levers and knobs should engage and disengage smoothly without trying very hard. The exception is the half nut engagement lever. This lever requires the leadscrew to be turning to allow the nut to engage. In this picture you can see a couple of things. One is the half nut lever and thread chasing dial. The second is the empty bracket on the right. This held a Trav-a-dial gage at some point. A very good question for the owner is whether they still have the dial unit and does it go with the machine. Major plus if they have the gage.
Also ask about tooling that is going with the lathe. Tool holders, tool posts, extra chucks and collets, drill chucks, centers, steady rests, follow rest. If its close to the lathe and looks like a lathe thingy ask about it.
If your still not sure take your camera with you and take A LOT of pictures including closeups and general shots or even video of it running. With modern digital camera there is no excuse for not taking more pictures than you need. My rule is when you think you have enough, take ten more. Give the owner a big enough deposit (check if they will take it) to get it off the market, or at least slow it down so it doesn't sell to somebody else while you check it out with somebody who knows machinery that you trust.