Other mistake: When they are in San Francisco, notice the pianist. The keys he presses don't correspond with the notes he's supposedly playing. It's a little bit obvious that the music was recorded in advance.
Other mistake: As they travail to The Pentagon in Washington, Carol and Dr. Marvin sit in the exact same mock-up of an airplane's interior that we saw earlier in the movie when a UFO passes in front of it. (00:00:45 - 00:27:00)