The prologue text at the beginning of the movie states that the documented footage of the secret Apollo 18 mission was uploaded to the website "www.lunartruth.com". If you type that address into your browser, it redirects you to "apollo18movie.net", which is the movie's official website.
(at around 52 mins) As Cdr. Walker's mental condition worsens, he mutters "Fate has ordained the men who went to the Moon to explore in peace remain on the Moon to rest in peace." This line paraphrases the beginning of a contingency speech, drafted by speech writer William Safire in a memo entitled "In Event of Moon Disaster," which was intended to be delivered by President Richard Nixon in the event that the Apollo 11 astronauts were stranded on the lunar surface without hope of rescue.
In some way, there was a real Apollo 18 during the year 1975. Named ASTP (Apollo-Soyuz Test Project), the mission was the first docking of spacecrafts built by different nations. The American crew included one of the seven Mercury program astronauts, Deke Slayton (the one who had never flown) and the Russian one Alexei Leonov, who was the first man to "walk in space."
The actual Apollo 18 lunar mission flight crew would have been the Apollo 15 backup crew: Richard Gordon (Commander), Vance DeVoe Brand (Command Module Pilot), and Harrison Schmitt (Lunar Module Pilot). Because of his expertise in geology, Schmitt was moved to Apollo 17 after Apollo 18, 19, and 20 were canceled.
(at around 18 mins) After the first resting period the astronauts are listening to 'Cheap Day Return' by British rock band Jethro Tull. Tull's third album 'Benefit' contains the track 'For Michael Collins, Jeffrey and Me', a song which refers to Apollo 11's command module pilot Michael Collins. In the song vocalist Ian Anderson sings about the feelings of the command module pilot, being left alone above while others get to walk on the moon, something which is also referred to during the movie.
at around 1h 14 mins) At the end of the movie the cover story is that one of the astronauts died in a training mission over Tallahassee, Florida. In fact, astronaut Clifton Williams was killed in a plane crash near Tallahassee while flying a T-38 jet trainer in 1967 (this movie takes place in 1974).