Factual error: The story is set in 1943. Jean and Phyllis shouldn't readily know who Jane Russell is, as she didn't become famous until her debut film The Outlaw was a box-office hit after the war, three years later. (Although The Outlaw originally had a limited release in the US [but not the UK] in 1943, it was quickly withdrawn by the censors and not released widely until 1946.) True, they could have read about this film in a newspaper or magazine, but considering the strict wartime censorship then in force, it is unlikely.
Plot hole: A line of dialogue in "The Curse of Fenric" indicates that the Russians planned to make their escape by "going to the North Way", in other words, escaping to Norway. However, the story is set in the summer of 1943, when Norway was under Nazi occupation. It would not be a smart idea for any Russian military personnel to head for Nazi-occupied Norway.
Revealing mistake: When Fenric (having possessed the body of Judson) knocks over the chess pieces on the board, watch one piece (The King) in particular. You can see a 'hinge' made of white sticky tape attached to the board and the base of the chess piece, presumably there to stop the chess piece rolling away onto the floor.
Deliberate mistake: One major mishap occurred just prior to editing, when a videotape containing various close-up and insert shots was accidentally wiped. At that point, there was no way that the director (Nicholas Mallett) could go back and rerecord the material, and so he was forced to work without it. This meant using footage that would usually have been discarded or replaced. The 'give aways' that reveal that Mallet had to work around the problems of the missing footage are (a) the lack of any close-ups of any of the actors in the final 10 minutes of episode 4, and (b) the continuity error involving the flames in the laboratory for the same period...the flames go from low to high and back to low from shot to shot.
Continuity mistake: Near the end of episode 4 of "The Curse of Fenric", when Ace and the Doctor run out of the exploding bunker, the Doctor stumbles in the mud and puts his hand out to stop himself falling, getting mud all over it. The Doctor even stops to look at his muddied hand, in an almost symbolic gesture. Then the director goes in for the close-ups with the Doctor and Ace, and when the Doctor puts his hand up to rub Ace's nose (same hand), it's perfectly clean.
Continuity mistake: In episode 3, after the Nitro-9 explosion which Ace uses to blow up the wall, sealing up the mine shaft, the wall is can be seen still standing, unaffected by the blast. However, after a quick cutaway to the Doctor and Ace, the wall has vanished completely by the next shot.
Plot hole: In episode 4 of "The Curse of Fenric", the weather is supposed to change for the worse and become very stormy. The Doctor and Ace are seen to be sheltering under an umbrella from the torrential downpour. Yet the skies in the background are bright, blue and sunny...
Plot hole: One sequence which makes little sense is when Ace triggers the booby-trap gas grenade on the chess board. Although the Doctor places a wastepaper basket over the grenade, the green toxic gas is very much present for the rest of the scene but does not harm either the Doctor or Ace, despite it being shown to have been lethal to the soldiers in a preceding scene. (NOTE: This error only applies the TV broadcast and the original video release; the error was noticed and corrected in 2003 for the DVD release of this Doctor Who story).
Factual error: The Naval base that features in "The Curse of Fenric" is supposed to be on the coast of North East England. (A line of dialogue in the story refers to Maidens Bay - two miles from the base - as being in "Northumberland". Yet all the maps and charts on the walls are of the coast of South-East England (Sussex and Kent in particular) which is 250 miles from where the story is supposed to be set.
Continuity mistake: In episode 2, when the Russian soldier is enticed into the water by the now-Haemovores Jean and Phyllis, watch his helmet, which he drops into the water as he moves towards them. When the camera angle changes to a shot of him from the front, we see his helmet slowly drift from directly behind him out to the right of screen. Then we cut to a shot of Jean and Phyllis, then back to the soldier - whereupon his helmet again drifts from directly behind him off to the right. Finally, when the other Haemovores drag him down into the water, look behind him and you'll see the helmet, sitting on the beach well above the waterline...