I have a 95 325i with 140k miles which I've had almost a year. I'll tell you what I've had issues with:
First car ran great all the way until winter. Once winter hit, shit broke down!
My altanator went out, but this could be because I added 2 JL Audio W3's with a couple huge amps and then a really sophisicated alarm.. I was probably asking for it..
Then I was having issues when turning slowly. Ended up being bad water pump which I'm told needs to be replaced all the time in e36s.
Then car started and then died immediatly on my one time and wouldn't start backup. Ended up spending 1000 on new plugs and wiring, new mass air flow sensor which needs to be replaced once every 75k miles.
Then about a month after that, car died on me again and wouldn't start. Found out that the car was randomly flooding either because of a fuel pump relay (which I replaced) or a sticky valve which I was told happens quite in bit with these cars in the cold. got a block heater and car has ran smoothe for 2.5 months now...
Brake light circuit error... spend 20 bucks on a new one and replace it...
The only advice I can give you is this: BMW's are the best cars on earth without a doubt, but be prepared to spend money if they break unless you do the repairs yourself. I know enough to be dangerous, yet I still perfer taking it to someone I trust. I owned a pos ford because of this and I've found that this is the easiest car to work on if you're familiar with cars. Go buy a chiltons manual for $20 and it'll save you a ton of money.
Also mechanically, these cars are the best, electrically, they have problems. Check EACH and every fuse in the car and I would recommend spending $50 and replace all of them with really good ones anyways. Good luck and post pics.