When he flew to London, the plane he took was a two-engine jet. In 1969, there were no two-engine jets flying transatlantic routes. A four-engine jet would have been used.
Hanging on the wall in Jonny's flat is a Who/Steve Gibbons tour poster from 1976 - seven years after the film takes place.
When Kidman is being given his initial brief, he is told that "In a few days' time we launch our 11th mission to the Moon". However Apollo 11 was not the 11th US Moon mission in that program, previously only Apollo 8 and Apollo 10 had gone to the Moon. Prior to that, the US had sent 6 Ranger lunar impact craft that were partly or fully successful, 5 Lunar Orbiter missions - all successful, and 7 Surveyor landers of which 5 landed successfully.