The usual stuff, it has had to withstand Canadian winters, but rust has not been a problem.
Mufflers, shocks, belts.
Electrical system seems to have a mind of its own sometimes.
The ceiling fabric fell down, had to be replaced.
The radio doesn't work anymore, but they don't play anything good on radio anymore anyways.
I'm surprised by how many 82's I see on the road in Toronto. They seem to be able to take a real beating, and my mechanic says that it's a breeze to work on, and that if I maintain it properly I should be able to put 500,000 Kms on it. I was really fortunate in that this really was a "little old lady's car" when I bought it, and she gave me a fantastic deal (ie I have cowboy boots that cost me more than this car)
They never put a 350 into a 1982 cutlass. The biggest engine available was a 307. You must have added the 350 or somewhere along the way someone did.