The '01's had motor problems, better make sure this isn't one of them. I heard it looks something like this when they go:
BMW has extended factory warranties on more than 17,000 M3 six-cylinder engines—a powerplant some owners have referred to as the “Engine of Damocles”—while it investigates the cause of a number of engine failures.
The standard four-year, 50,000-mile warranty is extended to six years and 100,000 miles on M3s, M coupes and M roadsters equipped with the 333-hp 3.2-liter engines. The extension covers vehicles with BMW designation “S54” engines built in model years 2001, 2002, and until further notice, 2003.
In a letter sent to owners in December, BMW confirmed “cases of damage to the connecting rod bearings resulting in engine failure” in the 3.2-liter engines. The company told owners it is “conducting an in-depth engineering analysis to determine the reason for the failure.”