why no means exhaustive or complete... the following problems creep on e36s.. most of which are cosmetic, but easily repaired
Drivetrain-
Cooling system. Radiator and thermostate are of plastic and get brittle with age and break. Impeller on the waterpump is the same. All can be replaced with metal parts for more money than stock.
Cooling fan. This can shatter and destroy the radiator and possibly your hood and waterpump. Usually caused by bad engine mounts allowing it to hit the shroud. Upgrade to an electric fan to free up hp and make the car more reliable.
Driveshaft donut of "guibo" the rubber donut gets old with age and can shred.. all cars that use this design have this problem. it is a maintance issue
High powered cars can rip their differential out of the trunk floor.. there are repair and reinforcement kits.. but they are expensive unless you can do the welding yourself
Nickocel (mispelled?) engines can use a lot of oil before failing. most were replaced under warrenty
Vanos. The valve timing dohicky on the top of the head can die due to bad (old) oil and failing seals.
interior.
Headliner can and will fall down. harder to replace on the coupes than the sedans and hatchbacks.. but still not a pig of a job. Upgrade the gray to black for a nice look
Door cards. The Leather will bubble and pop off from the centre. Fabric is a better choice if you can find it
Windows. The plastic slides stick and break, dropping the glass into the door. I take mine apart every year, clean out the old grease, and relube them. No problems
Sunroofs have some brittle plastic parts.. usually involving the tilt function. The lifting blocks and the part that slides the inner cover back can break.
Pixels. The displays for the on board computer, odometer, and radio can and die horrid deaths. they can be repaired if you are good with electronics.
Suspension.
The "lollipop" bushings in the front control a lot and lead hard lives. Usually when they go though, they do not leave you stranded.. just with really sloppy handling. Mine literally fell apart in my hands, but the car was still driveable.
Rear control arms are easily damaged.. especially if the car has been towed (they make convient tie down points to people who do not know better) but are easily repaired.
rear upper shock mounts. They go bad and will result in a "thunk" when you go over bumps. upgrade to e46 convertable mounts for a cheap oem fix.. or go all out for heavyduty aftermarket
Generally though, except for the cooling system, nothing on this list is more than an annoyance and will not leave you on the side of the road. 90% can be repaired DIY if you are handy with tools.
They are great cars, easy to work on, easy to drive and easy to drive fast and hard. The E46 is basically a heavier version of the E36.
They also do not have the rust issues of the e30. BMW got that part very well sorted