Light-flickers and camera/set-bumps. Difficult to prevent if you're not careful, but you'll never get a good looking film with them. You could try using sticky-tack or strong tape to hold them down.
When you did the slide kick, parkour and "barrel roll" tests, your camera angles seemed rough and the panning wasn't smooth. That one is rather tricky, I never did them a lot so I don't really know how one might improve there. Practice should help, but my only thoughts for the angles would be to keep it level and not rotated, but again I haven't done tricks like those that much.
Getting your animation smoother is also key. More steps in animation is the best way to do it, you might want to tweak the frames-per-second to make sure it doesn't go faster or slower than what you're aiming for.
If you're really into LEGO animations, you should visit some communities like "Bricks in Motion", they're really serious about this stuff and can provide some excellent advice and resources.
