+1 for possible faulty diff. Had similar symptoms, a distinct 'clunk' when moving off. New diff totally sorted it.
I've read elsewhere that the internal construction of their diffs is one area where BMW appear to be cost cutting. Well worth ignoring the 'filled for life' BS and go for regular fluid changes in my opinion...
E92 pre-LCI 325i - Ohlins R&T; H&R spacers; M3 strut brace; Swift thrust sheets; BMS clutch stop; BMS CDV; RE g/box mounts; Saikoumichi OCC; K&N; Cyba scoops; BMW Perf Exhaust; M3 rear spoiler; M3 white dash LEDs; LED Angels; LED side repeaters; BMW Perf black grille; CSL reps; SSDD carbon diffuser; Monster Wrap black roof