Acceleration Difficulties

I have a 1998 BMW Z3 2.8. It's the six cylinder with a manual transmission and 102,000 on the odometer. About 12,000 miles ago when I would downshit and accelerate out of a turn the car would kind of sputter hesitate and miss breifly before it started accelerating but since this happened only once every couple of weeks I let it go. Now it seems the problem has gotten severly worse. When accelerating from a dead stop the car sputtes and misses and feels like the engine is going to cut and then starts accelerating normally. This only happens after the engine has warmend up to operating temp. I recently changed the spark plugs about 3000 miles ago thinking this would make it better and there was a slight improvement. Before the spark plug change the car would sputter not only on take off but when I would shift from first to second it would sputter on acceleration from second to third and also when trying to overtake on the freeway it would also sputter. Now with the spark plug change it only does it on dead acceleration although I have noticed that when I am below 2500 RPMs in any gear and I try and accelerate the car sputters and cuts out hard. Could this be a fuel pump or filter related issue. My mechanic told me that my filter should be ok when he changed my plugs but I am not sure if he really checked it and I know he never looked into my pump.