It could be a combination of things (worn parts, etc.), but as others have mentioned, the steering on 2001 models was different from 2000. Many complained it being too loose and sloppy at the time, and BMW subsequently offered a retrofit for 2001 models, but that was a looooong time ago. In 2002, they corrected it.
I had a 2001 325i, and I now drive a 2005 330i - big difference in the steering for sure.