I have recently had a similar problem with my 92 325i. My car would stutter and stall while starting out quickly. Slow starts were fine and above 3000RPM the engine ran smooth, until you tried to accelerate. Then the engine would misfire and hesitate.
I have discovered that a common problem with the 1992 model year was the stationary injector coils by ZUNDSPULE were defective. A break on the secondary side of the coil caused rough idle and/or misfire under heavy engine load.
The defective coils can be identified by the date above the word "ZUNDSPULE", ie 91 M 01 year=91, month=January), any coil produced prior to this date could be defective.
You can diagnose a defective unit by removing the coil from the engine, twisting and pulling the spark plug connector (long rubber holder) and looking inside the coil for a green corrosion or broken pieces. If signs of either are present then a replacement is required $$$.
I replaced 2/6 (the others were replace sometime before I took ownership - Why?!?) which I bought from BMW. For a new BOSCH replacement I paid $130.00 CAD each.
Good Luck and I hope this cures your problems.
see Alldata, Bulletin #12 02 92 (3506)