After owning over 12 E36 BMW's from a 325 to a GT2, including 2 x 3.0 M3 Coupes, a 3.0 Convertible and 4 x 3.2 Evolution Coupes both manual and SMG, 2 with ecu remaps, and two with New Vanos units prior to purchase, I have learned a fair bit of about the breed and thought I'd impart some knowledge for all you ebayers looking to buy one of what I consider to be the best value sport cars you can buy for prestige, power, style, comfort, handling and practicality. Hope it helps.

Things to check on a E36 BMW M3.

Rear Shocker top mounts ( They wear out, check by lifting car up and down via rear arch)
Vanos (An obvious one. Evos have twin vanos, problems usually show round 45,000 Miles, but cars advertised as having a new one are not always a good thing. The usual issue is leaking solenoid seals, a good independent dealer can replace these for circa £250)
Exhaust (Rear box over £500 and Cats very expensive, they rust at front and rear, where they mount to exhaust pipe, check for blow) at
Tyres (For a good set of Michelin Pilot Sports (They handle best with these as were fitted std) youre looking at £600)
Side Mouldings (The M Sport mouldings have metal inside them, these rust and the clips break off, enure all mouldings are close the the body of the car)
A/C (Ensure the ac blows cold as the ac system is expensive to fix if theres a leak in the condensor unit, up to £500 if its too cold the ac does,nt run, this is a feature)
Window Mouldings (A simple job, but the side rubbers by the rear windows perish, makes the car look old)
Door Rubbers (If ripped, they are expensive to replace)
Electric Windows (Check windows go up automatically, if not the units that control the window stop may have gone, which is a pain as they wont close unless you hold down the swtich, and full closure alarms wont b able to close the window, nor can you on the key.)
Keys (Most M3's from 94 ownwards have chip encoded keys that have to be programed t match the car, so if you only have one key than can be expensive)
Alloys (If they have diamond cut alloys most reburbishers will not touch them, as the laquer comes straight off again, and also if they are damaged bmw charge alot for a new one)
Keys (The M3 uses transponder keys, so getting a new one is costly, ensure you have at least 2 and 2 alarm fobs)
Front end (Check the bonnet catches are not to new, as these often get replaced on front end shunts. Check inner wing seam welds, should be neat and match each other, make sure all original bmw stickers ore on the front slam panel, and inner wings. Make sure bumper lines up, after shunts they can be loose or uneven.
GearBox (Whatch the 2nd gear syncro, they can get worn when previous owners have been snatching 2nd gear in the 0-60 dash)
Clutch (A clutch will cost you a good £500 to fit, if the car has between 75K and 100K most are ready for a clutch)
Trailing Arm Rubbers  (The rubbers on the front and rear trailing arms tend to need replacing circa 75K Get garage to check for you.
Lamdba Sensors (There burn out round 60K and there are2 of them on each cat)

Check oil levels for the hydrolic system, as if its low it will pop out of gear, can suddenly select nutrel when driving and give the occasional erorr code on the dash. when warm get the car in sport mode (not manual) and drive it hard through the gear range, ensure the clucth doesnt slip.

Check for standard equipment, as a bmw cd changer connection lead if the car doesnt have one is a good £50.00 and a new cd unit can be £300. Ebay is obviously a good place to get things, but the e36 cd changers are rare. Look for signs of paintwork, usual spots are round edge of windscreen rubbers, under the rear lights on the rear 1/4 where the 1/4 meets the rear panel, and inside the fuel filler area. None standard exhaust tend to be too noisy, like the scorpion type as they drown at motorway crusing speeds, thornely motorsport do some good performance bits I belive.

Most of this stuff is obvious, but I've learned the hard way Hope its of some use.