The transmission for one. I am having it serviced right now so I am not sure exactly what the problem was. Since I just bought the car I am not sure what else will go. This seems like a car that may have a lot of problems.
I honestly love this car. Although it is not the fastest thing in the world, it still kicks ass. If this car was worked on it would be better. The car handles real well and has great luxury. The turbo is fun and has great pick up. It is pretty good on gas. As far as maintenance is concerned, I think that as long as the car is kept in good shape there should be no major problems. The only thing that no one can argue about is the sleek design.
There are anecdotal reports of motor mount problems on the '87 & '88 Turbo coupes as they age. I have read warnings to shore up the left mount, I think it was. If it breaks, you'll reportedly need a new intercooler and hood!