The windshield pillars are of concern on these cars, particularly the bottom corners where they meet the cowl. Rust is very common and so are quickie fixes. You don't want body filler hiding in the corners so check it with a magnet and go underneath the dash with a lamp as well. On convertible cars, the entire windshield frame is weak for rust. Check under the stainless steel header bar on a high dollar car. Replacing the A-pillars is possible, but it's a headache and a lot of money. Open the doors on a convertible car with the top lowered half way down. Both should open and close, no exceptions. You're checking for rocker panel integrity. If the doors give you trouble here, the body has rust in the rocker rail area and is flexing enough to change door alignment.
With the engines, the small block V8 is super reliable and a good one will give years of trouble free service. The 396 is also stout but much rarer. You'll likely encounter a 427 or 454 as a replacement engine on many cars. The main thing you'll be checking is how well it runs and was maintained. If the engine isn't running, have a mechanically inclined friend check it for problems.
The Chevelle four speeds and parts supplies are very good. Be aware that most of the Muncie's you'll see are M20 or M21 variety. Very few M22s were released during the 1966-67 era on Chevelles. You'll likely see Borg Warner T-10s and Saginaw transmissions as well.-
Verification: If you're buying a big dollar car such as a convertible, an L78 or L79 model, dig deep as you can into the vehicle. An original car with bill of sale and build sheet is the best kind of verification around but few of them exist. You'll have to compare the cowl tag, VIN number and several engine, transmission and rear axle stampings to determine if it is factory original. Your best bet for partial VIN numbers is on 1967 Chevelles. Prior to that, you'll only have an engine date code to check. The date code is stamped on the top front of the block near the water pump mating surface. The suffix code is below the passenger side cylinder head on a machined pad. It may be missing if the engine was rebuilt.
Serious collectors favor the '67 for styling and better chance of documenting original parts.
The transmissions have several part numbers that determine approximate age of the tail shaft, case and shifter lever cover. Sometimes a partial VIN is found on the mating surfaces of the case and tail shaft. One last place a partial VIN is found is on the firewall at the heater motor inlet. The motor has to be removed along with insulation in most cases. It's of no use on an air conditioned car unless it is stripped.
The rear axles have date codes stamped on the differential housing and application codes on the driver side axle tube facing the floor pans. You can also check the frame for proper date code and some even have partial VINs as well. The driver rear frame rail is stamped on top between the trunk floor and frame. You'll need luck and a dental mirror to find it. This should cover most of the big worries on a rare car and will help you grab that rare Super Sport.