During the launch sequence, the third stage is shown separating from the second stage (actually an oft-used piece of film from the unmanned Apollo 4 mission), but after this, we are shown the first stage falling away - an action which would have taken place before the third stage separation.
During the landing phase, one shot shows the view of the Apollo 17 landing site, instead of Apollo 11's.
All Apollo landings were done with the sun directly behind the lunar module.
The amount of remaining fuel was called at "30 seconds" and then "20 seconds". In fact there was not call at 20 seconds, and by about then the Lunar Module had landed, though it is shown as still being well over 50 feet above the surface, and not landing for another 30 seconds.
When Armstrong and Aldrin descend the ladder to the moon's surface, their steps make a pinging sound on the rungs. No sound can be carried on the moon due to it's lack of air.
A photo of a Saturn V night launch is shown. This is of the Apollo 17 launch (the only time a Saturn V was launched at night), which was in 1972. The Apollo 11 mission was in 1969.