Parts of my video looks like some of the objects have movement where there shouldn't be any. Any clue what's going on?

CCan you post a piece of video somewhere or something that shows what you're calling about?

I Don't understand your description either, but as an educated guess:

are you probably noticing compression artefacts = blocks/squares, esp in darker parts of your clip?

In addition to what Tom and Karsten said, you may also want to click the little triangle at the top right of the viewer, change from Better Performance to High Quality and see if it helps. If that is the case, then this is only a viewing problem that would not affect your export.

Are you talking about the the moiré patterning on the guy's jacket? These guys seriously need to learn how to get ready for the camera. Nothing you can do that's any good to mitigate it, short of blurring it with a tracking mask, but then it's going to just look ugly. There's also horrible interlacing artifacts that haven't been scaled properly. What are your exact shooting specs and project properties?

Also noticed lots interlacing artifacts on tiny details like railings. Just ignorant video guys. They'll learn.