Where to begin... here's a good link for you... BMW E36 DIY (Do It Yourself)
- Rear shock mounts, replace them if they are factory. Get the newer reinforced ones
- Rear trailing are bushings... can't remember how many times I changed these
- Check the rack and pinion
- Inspect the rear subframe
- Water pump... make sure it was replaced with a pump that has a metal impeller... stockies werre plastic
Stock speakers are okay, normally driving too fast to listen to music. I never changed the speakers on both my e36s. Head units were changed on both.
- watch for rust in the rear wheelwells towards the back of the car.
- inspect the wiring in the trunk coming out of the rear deck lid. some wires get kinked, some get exposed from rubbing eachother
- rear trunk lid locking mechanism may go haywire from time to time. In part related to frayed wires
- collision sensor likes to play games with your head when you hit bumps. repeatedly opens and closes \locks and unlocks\ doors while you drive
- electric windows like to stop half way and go. sometimes related to window switches sometimes related to position sensor in door (if I remember correctly)
- door latch on B pillar needs if locking becomes an issue. Visual inspection will reveal wear and tear
- wiper linkage needs to be inspected
- exhaust system needs to be inspected. not cheap to replace
I'm sure there is more. e36s are solid cars and I always wanted an e36 M3 but it never happened. The e46 came along so...
before you buy put her up on a lift and do a visual