When Morris is outside his home in the car looking at Fox in the side mirror, the image he sees is that of Fox and not himself.
During a meeting with the general and the Area 51 people, Fox, or Morris appearing as Fox, is told that the flight data recorder was taken from a scrapped F-111. The F-111 series didn't have flight data recorders during their service.
The sign at the gate of Area 51 is incorrect. The Air Force would NEVER post a sign calling that location area 51. The official Air Force name is the Nevada Test and Training Center.
Fox is dancing in front of the mirror which shows the reflection of the actual body he is inhabiting. When the wife enters the room, the reflection in the mirror is the real Fox instead of the inhabited body. This is due to being re-framed from its broadcast aspect ratio of 4:3 to 16:9 for DVD release and later TV sets, having been shot in 16:9 but only prepared by the crew for the 4:3 broadcast.