For all those that think driving at 1500rpm is really bad and/or will hurt your engine, I've noticed in D3 (DCT), it's will shift into 7 at a steady speed ~50mph/no accel, which I've noticed is around 1500rpm (or certainly less than 2k, IIRC). If driving at that RPM was that bad, I don't think M would have allowed the DCT to be programmed that way (unless low RPM in higher gears is better than low RPM in low gears). This is actually one reason I don't like the D modes that much. D3 is too granny, D4 is a bit too aggressive for everyday driving.
To the OP, I've definitely noticed low torque at those RPMs, but never any stumbling. Sound like an issue. Has this been happening for a while? Sure you don't just have a bad tank of gas?
2011 Jerez Black/Fox Red E90 M3 DCT, ZCP, ZCV, ZCW, ZP2, BMW Apps
2015 Golf R