The Drivetrain:
The engine is more-or less the same engine found in the US 535i, however with a few changes. Most notably is the compression ratio, and power output. Always check oil spray bar bolts at every valve adjustment, and keep an eye on cam wear. The M30 enines are really bullet-proof if maintained well. Always check for excessive oil consumption or oil leaks. Many drive-ability problems are caused by the FI Motronic system. Mostly there are sensors that go bad: ICV, coolant temp sensors, etc. Even well maintained cars can have these annoying, niggling problems. The good thing is that Motronics is pretty easy to troubleshoot for the average DIY'er. Don't be afraid to try to figure out what's happening yourseld. A good set of tools and a multi-meter always helps. And if you still can't figure it out, just e-mail Rob Anderson, the Technical Advisor. A chip will transform the car. Go ahead, splurge a little! The transmission is also strong, with no major problems other than worn second gear synchro's at high mileage. Always heel-and-toe, double-de-clutch downshift. If you practice it feels VERY good, and you save your transmission. Another good point is that Paul Wegweiser has a 2002 with a transmission well up into the 6 figure mileage range - around 200k. He got it when it had about 50k or so, and always double clutch up-shift AND downshift. I was driven in it, and it's still good. Redline does wonders to transmission operation in cold weather.
Brakes:
The brakes are ok with good pads. However there are some good modifications you can do to improve the already superior(relative to most cars) braking power. Regular E28 535i front brakes are single-piston, 282x26mm. M5 E28 brakes are 4-piston, 300x30mm. M5 brakes are a direct bolt-on to any E28 but you need to run a minimum of 15" wheels(some 15" wheels will not fit) for caliper clearance. E32 brakes are a cheaper solution. E32 7-series brakes are single-piston, 302x28mm and are also direct bolt-ons. About rear brakes, the only ones that fit an E28 are E28 M6 and any E34 5-series ONLY. Upgrades are for people considering autocrossing, driver's schools, or want ot have better performance all-around. General everyday driving is perfectly adequate on stock brakes.
The Suspension & Steering:
ALL front bushings need, and will periodically need replacing. No if's and's or but's. 750 Upper control arm bushings are a MUST. The steering boxes don't stay perfect for more than 60k or so, so you'll ALWAYS have a little slop. Learn to live with it - these are recirculating ball steering boxes - in other words, TRUCK steering systems. Be glad they work this well! If you do all the bushings at once, you'll be shocked at the difference. Trust me...
The Interior & Electrics:
New fuses, and cleaning all contacts are a must! ALWAYS do this before trying to solve any electrical problem. Battery, alternator, an starter cables are always a good investment at high mileage or old age. Of course, there's no substitute for a good multi-meter and your brain! New rubber gaskets for doors and windows reduce wind noise and keep the moisture OUT! A good thing. Leather seats should always be maintained - as far as cloth or vinyl replacements are much cheaper. Used replacement leather seats are a good bet(when you can find them(Rob A. is selling some)). Water in the trunk or interior is BAD. Get it fixed ASAP, otherwise rust can start. The exterior chrome trim is relatively easy to replace too.
Final Word:
There is a wealth of information on-line. Always check the archives, because chances are there have already been problems with that exact thing you have. Find a good, trustworthy mechanic to do GOOD work on your car. And save a few pennies and do some trouble-shooting and work yourself. It'll save you time, money, and you'll learn to enjoy your car even more. These cars have a few problems that affect them, but if you solve them early on, at once, you can enjoy your car even more when it's working at its optimum.