I'm not sure what you're trying to get out of this test, because I'm pretty sure that it's going to be a little jerky simply because of the way this is using a browser (as opposed to something made for 2d graphical movement...).
Anyway, mine moves across smoothly most of the time, but there are little jerks in between (in Chrome). It also depends on which browser I'm using. Chrome does small jerks every several seconds (a series of them) and then stays smooth the rest of the time, whereas Firefox has very tiny jerks with a big jerk every several seconds. In IE, it doesn't move at all. >_>;
As for the box shape, it depends on how quickly I make it move. Occasionally, the one of the sides (left and right, not up and down) seem to kind of "go inwards" for a bit (ie, the box looks rectangular-ish, since the sides go in a bit), but I think that's (again) simply because of how this is executing in a browser, and the movement isn't necessarily that smooth. Kind of reminds me of when I made some C code that went into a gameboy emulator. Basically, you had to clear off the screen once after every time the box moved, because otherwise it would leave a trail behind. I think there's a similar effect at work here, and that's what's causing the box to "change shape" as it moves. I also notice that there's a few "floors" included in there somewhere. I don't have time to trace the code, but I think that might affect its movement.
Edit: I think it would be more helpful if we did a test that was more easy to relate. If you want, you can download Wolfenstein ET (it's a free game), and then try playing with some people. Aside from obvious occasional FPS drops because of huge firefights in the engine (or internet lag), tell me if you notice anything strange. I can play that game without any problems...