mr. t
welcome to CAC.
a lot of what has been already described lends itself to preference and really doesn't answer your questions. that said, it is all very accurate, however, in my opinion here are at least a few of the things to look for in a 78-79 vette:
frame rust. look particularly in all the areas where cross members and front and rear frame extension meet. these are places that are particularly vulnerable. it is not unusual for the lower radiator support to be deteriorated, but that is not a problem as it is easily replaced.
check to make certain that all the foam baffles are still around the radiator. these block air flow around the radiator and force it through the radiator. if they are gone, chances are the car has been run on the hot side and not cooled properly.
look at the windshild frame where it meets the door jams for rust. it is also an area that is particularly suseptible to rusting.
if you are looking for a 78 pace car, make sure that all the "limited edition" package accessories are present (when i bought mine, a few of the power options that had either failed or been problematic along the way were just disconnected (if i was lucky) or just removed and discarded (which was more the case). some of the "replacement" parts used were functional, but not correct. you'd be surprised how quickly $80.00 turn signal levers that are the correct ones will add up, lol. if you are prepared for all the little things to make it right, and you factored it into the price you paid, all is well, if not, BIG SURPRISE, trust me!!
check the vin number (it's coded). all pace cars will have the last 6 digits starting with 9 and ending in a number NO MORE THAN 6502 (example 1Z87L8S906502). the "L" indicates the engine (in this case L-48). as previously mentioned go to the learning center for number interpretation. if the number after the "S" isn't a 9 you are looking at a clone and not an original pace car.
make certain that the trim tag is inside the drivers side front upper door jam. it will give you the coding for the original paint and trim combination (as compared to the current colors).
since the headlights are run on a vacuum system make sure they seem to work properly. try the over ride switch first before starting the car and trying the light switch. it may give you some indication that the system is holding a vacuum properly in the reserve tank and not leaking it out somewhere.
run your hand (carefully) inside each of the fenders and see if there seem to be irregularities inside that would indicate a fiberglass repair (accident damage??)
ask if the brake calipers have been either replaced or re-sleeved with stainless inserts. look for brake fluid leakage markings on the calipers.
see if the emergency brake seems to work (they all deteriorate very badly over time and freeze up or have been disabled or removed instead of being repaired and replaced). if it works someone has paid attention to it, and probably also to the car in general.
if you are looking for a nice vette to be a driver, numbers matching, etc is not that big an issue, but it is nice to have an original engine at a minimum, but that's just my opinion.
how long has the current owner had the car and why is he selling it?? (if he has only had it a short time, be weary of someone trying to flip a problem car they bought unwittingly).
just a few things to think about in my opinion. i'm sure there are a lot of others herre who can add to my suggestions.
good luck in your search. i've had C2 (1), C3(2) and C4(1) vettes and i am partial to the looks of the C3 as a head turner.
steve