Any problems would be related to the vehicle itself. Also, any info on the vehicle itself would be useful- auto, manual, 4 cylinder or 6?
As always, check that the tires match- if they don't, the PO (Previous Owner) is a cheapskate or an idiot. Either way, walk away. Also, check for rotting, cracking, bulging, uneven wear, etc. These all will require at least new tires, if not additional fixes.
Next up, check the oil- if it's DARK brown and doesn't flow well, they haven't maintained the vehicle.
If you're able, pull a spark plug- check the gap, condition, etc. If it's worn out, that's another thing you'll have to pay for. ALWAYS DIY fixes on a car you're buying- the PO will ALWAYS go cheap on the fix, leaving you with inferior products.
Check underneath before you fire it up for leaks, smells, etc.
Check the top for holes, cuts, leaks, etc. If they have a hose, spray it over the Jeep to check for sealing. A new top is a fairly expensive proposition, and a PITA.
When you fire it up, watch for extended crank, and listen for noises, sniff for smells, and listen for noises. If it sounds out of place, it likely is. Trust your senses.
Next up, before you roll, check for any leaks underneath.
When you drive, try out EVERYTHING. A/C, rear wiper (if it's a hardtop), window cranks, headlights and turn signals. Anything major (A/C isn't cold, heat not hot when warmed up, etc.) should be a deal breaker. If a turn signal is out, use that to bring the price down.
Also, find a dirt lot (if possible) to engage 4WD. A lot of folks never use it, so it may need R&R work, and this, too, can get expensive.
When you drive, don't just take a spin around the block. If they don't have plates on it, throw the ones off of your car on there and DRIVE IT! Take it on the highway to feel the power and transmission shifting. Floor it! Really get a feel for it. Too many people are timid about test driving, and this can hurt them. Treat it as if it's your own (within reason).
Do everything you can think of- take the top down, put it back up. If possible, wheel it a bit, even! I've done this on test drives, and it can make or break a sale. Anyway, best of luck, and fire away with any questions- Mark W.