At 2:24 Deke's blood is shown floating in space while in fact the rocket burn was still ongoing which would have caused continuing acceleration and liquid droplets would have appeared inside the cabin, to accelerate in the opposite direction - towards the back of the cabin.
The keyboard on the all the Apollos have an abbreviated "cut off" keyboard, missing several of the outer key for no apparent reason.
During the "P12 Ascent" sequence, Ed is seen punching random keys (both the 1 and the P keys are not there).
The SPS had a delta-V of 2800 m/s, which would have been even higher without the LM attached. This is only slightly less than the total S-IVB burn for TLI. The margins on the Saturn V were small, no way that the over-burn would have anything close to a velocity required to need to use the entire SPS fuel load to correct.
The whole sequence of Apollo 24 pulling the Apollo 25 capsule by the tether rope is complete nonsense. No rope can hold that kind of pull, or the grappling hook would have pulled the rocket open. Also super-strong Tracy could not unhook the line.
At 17:47 Russian cosmonaut is shown wearing an earring in his left ear. As all cosmonauts of that time were military officers, this would be a violation of a dress code and would have resulted in immediate dishonorable discharge.
Blood droplets emerge from an astronaut's wound while inside an accelerating spaceship, and the droplets float weightlessly rather than falling toward the back of the spaceship. Shortly thereafter, the thrust stops and the astronauts themselves start (correctly) floating weightlessly.
The lunar module couldn't dock with the CSM because it was wobbling, not because it was too far away. Ed could have just got up close to it and virtually passed the fuel across, instead of throwing it from hundreds of metres away.
When Baldwin blasts off to rescue Apollo 25, Jamestown Base remains unattended. By international law it would be an abandoned shipwreck, and the Soviets could immediately claim it. It makes no sense why they didn't, particularly as Mikhail Mikhailovich is standing next to it, very much aware of the situation.
When Apollo 24 returns, Molly walks up to Margo to tell her about Apollo 25's shortwave antenna. But why did she wait with this critical information until landing? She could've reported it by radio.
When the NASA administrator tells Marge Slayton that Deke has died, the entire mission control team is shown watching. There's no way they would all abandon their stations when a critical operation is underway in space.
After Ellen regains consciousness in the runaway command module, several times she doesn't move like she would in zero gravity. At one point she sits down by dropping herself which wouldn't be possible in space. The acceleration of the rocket wouldn't explain this.