As the title says BMW's (93 E34 525i M50B25TU) engine misbehaves in low gears, namely in 1st and 2nd, most of the time when the engine is cold but sometimes even when it is properly warmed up. The symptom is that even with half throttle the car either doesn't accelerate or jolts, this usually happens between 2000 and 4000 rpm, after that everything is OK, in 3rd or higher gears this doesn't happen even when the engine is in the critical rpm domain. What could be the root cause?
It sounds like the VANOS seal has failed. The M50TU has a single VANOS that adjusts cam timing at a single point based on RPM. Here is a good article describing the failure symptoms and the repair procedure.