Just before the playback of Ellen's video we see Mozzie's finger operate the Play lever (second from the right) on the Betamax VCR. A subsequent shot of the VCR shows that the lever is no longer down even though the video is still playing on the TV.
When Neal is laying on the ground after the knockout blow from Peter, Mozzie throws the towel into the ring which lands on Neals' stomach. In the next shot, it is now laying next to him despite Neal not moving.
Elizabeth is shown driving a car with US government plates. As a civilian, she would not be authorized to operate one. Additionally, the FBI does not use cars with US government plates as shown.
Neither Peter nor Neal wear mouth guards during their fight, because the actors have to deliver dialogue.