Welcome to the Werkz and glad you found a reason to join. I'm assuming your 1981 is an E12 and if that is the case I know some of the common issues with that generation of the 5-series were mostly electrical, the air conditioning was weak by American standards, and I know many parts of the the car had to be modified to bring it to USDM specs from DDM specs.
Some of those changes included bumper reinforcement (US regulations demand a bumper withstand a 5MPH impact with no damage to the cars body, the headlights had to be sealed, and I also believe the engines had to be modified to meet US emissions laws. However, you're lucky as the 528i was BMW's replacement to the 530i which suffered from issues related to emissions control and I know for a fact the 4 speed manual was replaced with the 5-speed manual in 1980.
Since your E12 is essentially a last year production vehicle I'd assume most of the issues were likely worked out in terms of annoyances. However, your car is 19 years old and it may suffer from issues here and there. Assuming it's been well maintained you should be fine. Any questions feel free to ask and I'm sure someone will answer your question.