Basically I got the same problem as everyone in this thread:
SMG 1st Gear Shudder - Solved - BMW M3 Forum.com (E30 M3 | E36 M3 | E46 M3 | E92 M3 | F80/X)
I thread through the whole thread and saw like 10 different solutions from chainging tire pressure to a full clutch replacement.
Has anyone ever experienced this? I'm pretty confused upon what to do to fix it. I'm leaning towards changing my fuel pump..
E46 M3 Fuel Pump - Turner Motorsport
"A fuel pump failure in the E46M3 can cause lack of power and a low-RPM stumble. Its a fairly common problem, the problem fades away as the revs build and the engine warms up. It's especially noticeable in the Winter and when the outside temperature is low. While a number of things can cause this, you should first change the fuel filter (especially if it's been over 30,000 miles. The fuel pump is another likely source of the trouble. The pump is easy to change by accessing the top of the fuel tank under the backseat. This is a new factory BMW fuel pump."
OR
SMG RECALIBRATION <- Anyone done this?
It's really bad when the "studder" kicks in while going uphill. If you have experienced this in your M, please provide details on how you fixed it! Thanks!