Check the fiberglass leaf springs, front and back. They are transverse, and coated with a protective polymer. Solvents or sloppy torch work on the exhaust will damage the coating and allow the fiberglass to erode.
I wouldn't worry too much about minor stuff. Check the compression (relative, by measuring cranking amps vs. time on a digiscope, so you don't have to pull plugs) and for oil/trans fluid leaks. c4vettes.com has a good buyers checklist (as does this site) but they also have a nice procedure for starting/shutting off/restarting that will spot leaky valve guides or bad rings. You basically need to start it from dead cold. If you ask him to not run it overnight and then it's warmed up first thing in the morning when you get there, he's hiding something.
Make sure the heater/defroster works. You don't want to replace either core if you can help it.
Ask for maintenance records.
Check for play in the rear bearings (pull the wheels in and out), good is 1/16" or less (?)
Check the footwells on both sides for cracks/holes in the fiberglass, right where it goes from horizontal pan to up at a 45 degree angle. You have to take up the carpet to see it from the inside, but it can be easily seen from the outside it you know where to look. Not a hard fix either.
The cars are pretty easy to work on. I just got my first vette (first convertible also) a couple of months ago and it's like every day is christmas. Buy as much as you can as soon as you can. Drive it hard on the test drive. If he won't let you, he's hiding something. If there's a problem, it will show up then.
Also, as it's a vert, try to see it in the rain to check for water leaks into the interior. The hood latch, cowl, and evap core drains often clog up and water gets in by the footwells. Those are all easy fixes once you know where they're located.
Good luck!
