Visible crew/equipment: In episode four, after Marcus opens the second door in the pyramid (the one with the hidden switch), someone wearing a white shirt can be seen through the opening.
Revealing mistake: The "crystal" tube holding Sarah wobbles whenever it is touched.
Continuity mistake: When Sarah Jane is sitting on the floor inside the transparent tube and the two gold-trimmed mummies/guardians appear in the background, you can see the dust on the surface of the tube change noticeably as the fade occurs.
Plot hole: It is never explained why so much of the story takes place in England. All of the equipment for Sutekh's rocket comes from his tomb and could just as easily - probably more easily - have been set up right there in Egypt. And at the end, instead of just walking out of his tomb, he takes the spatial corridor to England just so he can get caught in the Doctor's trap.
Factual error: The Doctor states that the radio waves take two minutes to get from Mars to Earth. The time interval can vary dramatically depending on where the two planets are in their orbit. But at absolute closest approach, Mars is just over three light minutes from Earth.
Continuity mistake: In the first minute of episode three, one of the evil robot mummies attacks Sarah Jane Smith. In doing so, it lunges forward, misses Sarah Jane, and smashes the "Marconiscope" device, which explodes in flames. However, seconds later, the 'Marconiscope' device is still visible in the next shot, but totally undamaged.
Plot hole: Why is the warning about Sutekh broadcast in English? (It clearly is as the Doctor identifies three E's in the transcript).
Continuity mistake: In episode 3, when the Doctor leaves the old house to find the dynamite, you can see his hat resting on a chair as he walks out the door. Immediately afterwards you see him walking through the woods with Sarah, and see that the hat has magically relocated itself to being back on his head again. And when he eventually gets back to the cottage, the hat is there, still in the chair as if nothing had happened.
Visible crew/equipment: Episode 1: After Sarah teases the Doctor a bit when he's being somewhat moody, just as the TARDIS is suddenly thrust off its flight path (which was back to UNIT), Sarah and the Doctor are thrown about in the wonky console room (because the camera turns sideways), and the second camera becomes visible at the left side of the screen.
Continuity mistake: The Doctor's hair goes from being messy and extremely curly in the TARDIS scenes to being combed and much less curly in the scenes set outside the TARDIS.
Revealing mistake: In order to save money filming the lift-off of Crayford's rocket from Oseidon, the producers decided to use stock footage of a Saturn 5 blast-off. Unfortunately, that meant the words "UNITED STATES" in large red lettering are seen on the side of the rocket...which is a little bit of a giveaway, especially as the rocket is supposed to be a BRITISH space probe.
Visible crew/equipment: In episode one, the Doctor and Sarah crouch behind a pod to escape the android laser fire. They lie on a large brown piece of cloth conveniently placed to keep them from getting dirty.
Revealing mistake: When the Morbius creature falls over the cliff, he bumps into the camera.
Revealing mistake: The fake snow in episodes one and two is effective - with the exception of when the Doctor is digging up the second Krynoid pod, where it is painfully obvious the snow is styrofoam packing peanuts.
Plot hole: At the very end, the TARDIS materializes in Antarctica and Sarah comments that they've returned. But the TARDIS was never there - the Doctor and Sarah went to Antarctica by helicopter.
Suggested correction: But THEY were there.
The Masque of Mandragora - S14-E1
Factual error: Giuliano explains to Sarah that he thinks the world is round as though this were radical. But this was the common belief throughout the late Middle Ages. The argument was about how big the Earth was and the ignorance about the existence of a continent between Europe and Asia.
The Masque of Mandragora - S14-E1
Factual error: Giuliano makes references to the invention of the telescope. Yet the invention of the telescope was at least a century after the events in the story and Galileo's experiments more than 50 years after that.
The Masque of Mandragora - S14-E1
Continuity mistake: When the Doctor is explaining about the Mandragora Helix, his scarf goes from being over his shoulder, to behind his shoulder and back.
Factual error: The nuclear physics in the reactor scenes is laughably incorrect.
Visible crew/equipment: After Rokon's message in episode four, Eldra starts ranting and raving. A BBC camera can be seen in the doorway behind the Doctor and Sarah.