Once upon a time, I acquired a 1983 BMW 533i for $500 on Craigslist.
Here are some notes:
Issues I ran into include:
A power drain caused by the door light switch shorting out.
Very simple five minute fix.
The crank position sensor went out which caused the car not to run. Very simple and quick fix.
The automatic windows needed to be greased to roll up and down smoothly. A few hours worth of work.
The instrument cluster had issues with the mpg gauge so it was replaced. Junk yard find and 30 minutes to fix.
Many think that BMW's are hard to work on, but in reality, they're really just like any other car.
According to the 2008 Collector Car Price Guide, a very good original example of the '84 533i should is valued at ~ $8500.