+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; Meyle HD droplinks; BMS clutch stop; BMS CDV; RE g/box mounts; Saikoumichi OCC; K&N; Cyba scoops; BMW Perf Exhaust; M3 rear spoiler; LED Angels; BMW Perf black grille; CSL reps; SSDD carbon diffuser; Monster Wrap black roof