Nothing major:
The temperature light would come on after it rained out, but couldn't find anything wrong with it, and it eventually stopped.
The windshield washer fluid container leaks.
The ceiling covering is caving in.
I absolutely love this car. It's actually the 3rd Celebrity my family owned. I learned how to drive in a Celebrity and eventually inherited the last Celebrity. I'm a Chevy girl at heart.
This isn't a "little" car, and it's only a 4-cylinder, I'm surprised at the pick-up it has. It drives awesome, and it's comfortable to drive. It's pretty good on gas too, 16gal tank, usually filling it up every 1.5-2 weeks and I commute to work.
Considering they haven't made any Celebrities in over 10 years, they are still tons of them on the road. They last a long time if you take proper care. And best of all they're cheap.
I have a 1987 Chevy Celebrity, 4 door sedan with a 4 cylinder in it. Only major problem I've had with it is a high idle problem since I've had the car. Only thing left for me to change out to try to get it under control is the throttle body. It's an awesome car other than that, I love it.