You seem to be working with interlaced video that isn't being interpreted correctly.
See this video for details about fields and interlacing:
Ahh, I had a feeling it had something to do with interlace. Had no idea about those interpret settings. Thank you so much.
You should not be using mpeg files in production unless they are camera originals. You could have introduced all kinds of artifacts and interlacing errors. Frame rates could be off. Without knowing your export settings or your comp settings we can only guess what's wrong.
For intermediate renders pick a production codec and stay away from MPEG of any kind in production. As Todd said, check you original footage, make sure interpretation is correct, and then render the stabilized footage to any production codec like Jpeg2000 QuickTime or even an image sequence. Also, make sure that you are using the right frame size for you render. I have no idea what the comp settings are so I can't help answer the question about composition settings.