As the lunar module lands on the moon, Aldrin is shown on the left side, which is the Command position, with Armstrong on the right side. This is the reverse of how they were in reality. Furthermore, Armstrong is shown clapping Aldrin on the arm and calls him "Commander". In the end credits all three Apollo XI astronauts are named Commander (a military rank none of the astronauts held -Collins and Aldrin were Air Force colonels). The upshot is that in this fictionalised version of Apollo XI, Aldrin commanded the mission and landed the craft, while Neil Armstrong still makes the historic first walk on the Moon. With the roles reversed, Buzz Aldrin had actually campaigned internally within Nasa for this to be how the mission took place; i.e. that with Armstrong being in command, it would be Aldrin to make the first exit through the door. The film's reorganisation of the positions and ranks may have been made at Aldrin's suggestion, since he was involved in the picture.
This was the last movie reviewed by Richard Roeper during his tenure as a film critic on Siskel & Ebert (1986) (which had been renamed "Ebert & Roeper at the Movies" following Gene Siskel's death). Roeper and his co-host, Michael Phillips (who was substituting for Roger Ebert) both gave "Fly Me to the Moon" a negative review. (Philips would return to co-host the show with film critic A.O. Scott, before it was canceled in 2010.