Pretty darned awesome!
I'm guessing the images is about as steady as can be achieved with Legos but I wonder whether building a film gate into the projector would improve it. A pair of vertical guide wheels could reduce weave by constraining horizontal motion of the film. A film trap with tension bands could improve vertical steadiness by creating friction which would reduce the tendency for the film to overshoot or undershoot the projection aperture as each frame moves into position.
He did pretty well with the shutter. Hardly any flicker or ghosting. That might be hard to tell from looking at the video but, from what we see there, it's still pretty good.
A film gate could be created with a 3-D printer. Done carefully, it could snap right in.