I have a 2001 325i and was getting the same fast flash to slow flashing blinkers on the drivers side rear, also getting the dash warning light. Then the brake light failed. I replaced all the bulbs to no avail.
I found out that a common problem with this model is that the the fixture where you plug the wires into the lighting unit in the back is prone to short out.
The car is 11 years old and the plastics just disintegrate causing a short. I ordered a "Part #: 61 13 8 369 TAIL LIGHT BULB SOCKET WIRING HARNESS PLUG REPAIR KIT $27.95" from Bavarian Autosport, it came with complete instructions and was an easy fix, even though I don't know a thing about wiring.
FlickingSwitches, my first suggestion would be to buy the Bentley Manual for your car. they are expensive, but well worth it. They have plenty of photos and diagrams, I have very little auto repair experience, but between the forums and the manual you should be able to handle most small repairs and fixes.
I'll try to get some photos posted tonight.