2002 BMW 330xi - wierd noises

When I'm driving on the highway for a while (more than 10 miles) my car starts to vibrate/shake when I accelerate. When I take my foot off the accelerator, it is very smooth, but when you step on the pedal again, it starts to shake. Its pretty freaky.

Also, when i make turns, sometimes I hear a clicking noise, especially on tight turns.

Any ideas as to what is wrong? The first mechanic told me to replace the wheels and I have done that and there is no difference. I also rebalanced the car and still there are problems. Any help would be greatly appreciated.

Thanks

Rizan