I just saw this and had to laugh.

AH.
it's late but you made my day with this.
Come on, you made that for a joke.
I mean why does the middle layer get a seizure und why does the top center rotate?

No, that was certainly not me. The real funny thing is that the comments say this was his 1000th attempt!

That was actually one of Oskar's puzzles-under-construction (the Seizure Cube, which would have been available for $374 on Shapeways), but it gained sentience after a freak lab accident and ran away, only to end up being filmed and mocked.

There's two things that are happening:
Each piece has a rotation in X, Y, and Z between 0 and 360.
However, when you move the pieces by hand, a rotation of 360 gets changed to 0.
So Those pieces are rotating backwards 270 degrees when they should rotate forward 90.

Also, there's something called "Gimbal Lock".
(http://www.youtube.com/watch?v=zc8b2Jo7mno, watch the video for a good visual explanation)
The way Euler rotations work, you first rotate something in the object's X axis, then the Y, then the Z.
The problem is that when you rotate along the X axis, the Y and Z axes rotate along with the object. And if you rotate the Y axis, the Z axis follows the object but the X doesn't. Most of the time, this doesn't cause a problem.
However, if you start with a 90 degree rotation in Y, you make it so that the X and Z axes are pointing the same direction. So with the X and Z pointing the same direction, and the Y pointing a second direction, there's no axis to twist for the third direction.
There's something called a quaternion rotation that fixes that problem. Unfortunately the numbers aren't really intuitive.

Interesting, but it's completely ruined all the fun.

Sorry. I tend to take a long time to write my replies. Everybody started having fun while I was still searching for a good youtube video
I tried to animate a 3D Rubik's cube at one point in college, and that exact problem showed up.

Hey no worries, i did find your post very interesting, and also your video link.

I personally think this is the worst Rubik's Cube animation ever.

http://www.youtube.com/watch?v=LYs_GCy9PRk