Okay. As far as I can tell, the rpm gauge doesn't go up at all before the car starts moving. It does seem like there is some power lag or something. Hard to put a finger on this one. I did however manage to capture some video that may help a lot. I should have turned off the stupid radio but I forgot. And excuse the fact that the video is sideways.
clutch? - YouTube
As you can see in the video, the rpms jump significantly then again by a smaller amount, then again by a tiny amount. This is what I believe causes the car to shake forward and backwards everytime it catches. I doubt it is the wheels spinning because I don't hear that at all and it happens even at lower rpm where wheel spin is impossible it's just not as obvious on the gauge that it is slipping. When I get higher like in the video, it jumps more and you can clearly see it. All I am doing is going to an RPM, letting off the throttle for a second, and then punching it full throttle.