Similar issue with 2001 530iA
No ideas right now, but here are my symptoms/info.
Car has 150K, however BMW replaced tranny at 100K. ZF tranny with life-time fluid and I have not changed it.
A few months ago I noticed when I slowed down to make a turn, and began to accelerate the car would skip/ hesitate/shudder. Later I noticed it would do the same thing when pulling off from a stop. On long trips it appears to act up more and feels more like a tranny slip. This is all intermittent and only happens a small percentage of the time.
I have researched and most suggest checking fluid level. I have the procedure and will try this weekend.