The rear frame rails and the backing plates rusting out were a problem with these cars.
I had both problems as well as the wheel cylinders and brake lines.
Both gas lines were replaced and the gas tank always leaked.
The water pump was replaced twice and the radiator needed replacing when the car died.
The rocker panel trim was always falling off and the horn always cut out.
The timing chain was the reason the car is in the wrecking yard as I speak.
The floors were rusted out.
The instrument cluster was replaced and the windshield was cracked.
I would love another 1981 Buick Regal, but in better condition and one I don't have to do a lot of work on.
Body wise the car looked good, but always look for the rear frame rails going and always check for floors and rear backing plates rusting out on the GM G bodies.
The older models had problems with the rear frame rusting due to small drain holes plugging and holding water in the frame. Later models came with large drain holes that won't plug up. If you like these cars buy a newer one say 84 or 85 and look for the large drain hole on the bottom of the frame just past where the frame rails curve for the rear wheels.