At 16:58, the camera is looking out from the window of the lunar module model, at Tom Kelly (Matt Craven) looking in. You can plainly see down to his shoulder as he moves, that he is wearing a white shirt. When the shot cuts to an outside view of Kelly, he's wearing a jacket.
The first stage of the Saturn V, shown at 39:02, shows it's serial number as S-IC-6, which belonged to Apollo 11. Since this is the Apollo 9 flight, the first stage serial number should be S-IC-4.
When Astronaut Rusty Schweickart is shown entering the LM for the first time while in space, as he drops into the LM the NASA patch is on the left side of his space suit, the mission patch is on the right side and the US flag is on his right suit sleeve. The "NASA" letters on the patch are clearly seen reversed (mirror image). The "SCHWEIKART" patch over his chest is also clearly reversed. Later, after he has entered the LM and secured his boots to the Velcro on the floor, we see the NASA patch on the right side of his suit, the mission patch on the left and the US flag on his left suit sleeve. The "NASA" letters are now reading properly from left to right, as is his name patch.
When Astronaut Rusty Schweickart is shown entering the LM for the first time while in space, he looks out the LM window, you can clearly see light from the cabin, where the window frame, connects to the spacecraft.
At approximately 27 minutes into the episode, as the astronauts arrive for the testing of the LEM, the onscreen graphic misspells "Grumman" as "Grummen".
At 32m 03s the passage of time is shown by the number of balls on the building roof. These are all very close to the edge, whereas the way they were thrown would imply they should be much further from the edge if the thrower missed.