high quality video morphing

Duplicate the layers you want to speed up and distort, separate out a bunch of the segments with masks, add some edge feather, distortion, blur effects, and time remapping, then transition between shots using multiple copies of the layers. The key to making this work well is to plan and execute the ending of one shot and the beginning of another shot with the transition in mind, so the camera is moving properly, the actors are moving properly, and the light is coming from the right direction. There is usually some key element in both shots that you can spin around, like the actor's hand or the magic wand or the teleporter (beam me up, Scotty). The better you plan and execute the shots, the better the transition will be.

If you are stuck with general footage, I suggest Radial Blur + Scale + rotation + opacity animation and maybe some blend modes between shots as a starting place.

The answer is pretty much the same as your Harry Potter question: Re:Flex and Twixtor Pro in conjunction with lots of drawing masks and tweaking the timing. In fact the soccer shoes example isn't even that complex and parts of it could likely even be done with AE's basic Reshape effect, though you still would need to figure out the correct sequence and likely will bump into tons of issues e.g. when paths gave different vertex counts because the effect doesn't handle it that well.

Mylenium