1992 BMW 525 stutters at low RPMs

I have a 1992 BMW 525. It is stuttering at low RPMs when I accelerate, and it occasionally backfires. My mechanic has changed the fuel filter, oil filter, and air filter, and he cleaned the injectors and replaced a damaged o-ring in one of them. Although cleaning the injectors improved responsiveness at higher rpms, the car still stutters below 1500 RPMs, especially when I try to accelerate rapidly. The stuttering seems to lessen slightly as the car has been driven for longer. The car also shakes slightly, and the engine will occasionally surge after being started.

Thanks for your help.