Corrected entry: In the shot where Jim is with Marilyn, outside of their house right after the Apollo 11 landing, he blocks out the moon with his thumb. In the final shot, where he puts his finger in front of his face to hide out the moon again, you can see the shadow below his chest. It should be on his eye.
Correction: The only porch lights visible in the scene appear to be behind the actors and were a yellowish color. The light on both characters faces is white and intended to portray the moonlight. Even if the 2nd source of light was shining right on Lovell's face, the white light of the moon would have cast some kind of shadow from his thumb over his eye, particularly at the start of the scene while he was standing up. During that sequence, no shadow of his thumb could be seen anywhere, not even on his chest.
Corrected entry: As the spacecraft nears Earth the men in Mission Control remark that its angle of approach continues to wander away from plan. They figure out that it's due to the absence of the originally planned mass of moon rocks. This is wrong in several ways. First, it could not wander off course while coasting due only to the vehicle mass. From the time of Galileo it's been known that objects fall with equal acceleration (at a given distance) regardless of mass. Indeed, if that were the reason then the mass difference would not just be a lack of moon rocks, but also the extra unplanned mass of the entire lunar module. The actual reason was simply the slow leaking of gases from the damaged vehicle, acting as a low thrust rocket motor pushing it sideways. (01:53:20)
Correction: As the men at mission control assumed it was due to moon rocks at the time, the film was just repeating what they said on the transcripts. So it is not a factual error.
Correction: Actually it wasn't a leak due to damage, but due to the LM's steam sublimator (cooling system) giving a tiny thrust.
Corrected entry: During liftoff, one of the five second stage engines fails. This is indicated by a shot of the control panel, and one of the five indicator lights is flashing with a buzzer going off loudly in time with the flashing light. In fact engine failures were indicated by having a light simply go out, and there was no buzzer. Director Ron Howard originally shot the scene accurately, having a light just turn off was visually uninteresting and did not convey the drama of an engine failure. After getting the OK from Astronaut and technical advisor Dave Scott, the more dramatic indication was used.
Correction: Artistic decision to convey the drama and assist the audience, not really a movie mistake. A typical embellishment which is quite permissible in movie world.
Correction: Actually the indicator lit up if an engine was generating less than optimal thrust (ie a shutdown) While you are correct it did not flash or set off a caution/warning tone, all lights would have been extinguished and 5 would be lit with a solid light.
Correction: This is one of the most frequently quoted "non-mistakes" of Apollo 13. It is valid only if the moon was the ONLY light source in the scene, and it is not. There are three or four strong porch light to screen right. Moonlight is pretty feeble and the lights cast the far stronger shadow.