There were a lot of problems with the early '89 doors, including not staying shut. I remember driving to work in the winter using my right hand to hold the door shut while I steered with my left. Shifting was a problem! At some point they redesigned the latches and BMW told me they wouldn't fit my early 525i without new doors! I thought that wasso we ordered a full set of latches and installed them, under warranty, in the old doors, with no problem.
It's also possible yours are just worn out. I've used electrical tape over the cylindrical part of the latch to keep the latches from rattling and mine is a 1995 model.