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.
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.
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.