Lots of glitching going on there, and there's only a couple of things that cause it:

1. Corrupt replay file - not something that happens a lot.

2. Too much editing.

Sometimes the game remembers things you did before you edited & saves them along with the changes, so it jumps about & other weird stuff.

The easiest solution is not to edit or do it less. If you really wanted to you could manually clean up the replays. It would mean noting down every frame that the replay screws up on, then opening the replay file in notepad & removing the saved information for those frames.