It is probably a little late to be asking these questions. You are supposed to be looking for problems BEFORE you purchase the car. Well here is hoping you didn't get screwed. Fiberglass cars do rust.
1. Rust-you are in the rust belt. Look at the area in front of the rear wheels this is known as the rear kick up and is prone to rust and could cause your car to break in half. Check this area and where it goes up and over the rear wheels. Tap it with a small hammer or poke it with a screwdriver and hope you can't poke a hole in it.
2. Rust in the birdcage. Remove all the interior trim from around the windshield and look for rust. Also remove the kick panels inside the passenger and driver doors and check there also. Very, very, very expensive repair.
3. If your barke calipers leak they need to be rebuild the car is unsafe to drive until they are rebuilt.
4. If ythe car has 101,000 miles on it and the interior is perfect it is not the original interior. That is not a bad thing.
5. If the spedo doesn't work it probably has a lot more than 101,000 miles. Remember this car is 30+ years old and was driven for a good part of that time. Documentation is only as good as the guy who made it up.
With all that said good luck and welcome to the CAC and the Corvette lifestyle. Enjoy your car you will learn a lot, get your hands very dirty and if the bankbook holds up have a blast. This and other Corvette forums will provide you with a wealth of information all of which was learned from experience.
If you want to know what you should have done check out these websites:
http://www.corvette-101.com/
http://www.c3sharktank.com/tech2/tech2.html