Check the mount for the steering box, it connects are three points. 2 of them make a nice pivot and the pot metal 3 point breaks. There is a great kit to fix this, around 60 bucks.
Check the wheels, make sure they aren't the metric ones, pretty easy to tell as the tire size will seem very odd.
Get the car up to 60 or so, does it shimmy?
1) steering fix from above
2) upgrade to the 7 series bushing on the control arm
3) somebody grabbed a set of cheap 5 series wheels from that year that BMW ran a different bore on the wheels.
If it has self-leveling suspension, prepare to replace it with standard sixer stuff.
The rear diff bushing like to fail, its the easiest way to tell that your subframe bushings are going to fail. The are annoying to replace, the diff bushing is a joke.
Weird thumping noise? time for a new drive-shaft. If possible visually inspect the center bearing on the 2 piece drive shaft. There is a rubber isolator in there, it fails; time for a rebuild driveshaft.
Check the condition of the brakes, it may/should have a hydraulic instead of vacuum assist. Most notable from the report rock hard pedal (only thing from the above list that I haven't had fail on my 6)
Plug wires, price them... then go get a set of after market full silicon racing ones in 10mm for 1/3 the price.
If the car wont start, and you were anywhere near the firewall on the driver side, you just disconnected the CPS, plug it back in.
Check the heat, it can either be the heater control valve (located on the firewall by the CPS connector.....) its cheap. Or it the temp sensor for inside the car...its waaaay not cheap.
Air conditioning, the compressor is good. When it squeals like a pig, tell the ac guy to manually fill it with oil. Better yet, tell him to fill it with oil before he calls you on the phone and ask you to diagnose the squealing in the background.
The steering hydraulics leak, keep a quart in the car. Mine likes dextron something or other synthetic. The power steering reserve has a filter type element/screen in it, clean it.
The front bushing need to be re torqued after the weight on the car has been placed on them, then re-torqued again. Basically check them a lot after install.
The factory radio has a code, make sure you have that code. Replace all the fuses now, or at random intervals during your first road trip.
Check the aux cooling fan, when working properly it will draw too much current and melt the fuse box. When working improperly, you get to play watch the temp climb at the drive through. Yours probably does not work. Yours may have already melting portions of the fuse block.
The passenger window doesn't work because A) the switch in the center console is bad, test this by swapping it with one of the others B) the connect in the door is fouled, spray it with wd40 to test C) the motor is shot and you get to go junk yard hunting.
That's all I can think of, and remember mine was a M6 so not all this will apply to you, but all of this has happened to me except for where noted.