Factual error: The rank insignia of the Soviet officers is completely inaccurate. The captain wears the epaulets of a captain first rank (captain) and the sleeve insignia of a captain second rank (commander). Lieutenant Stephashin wears the epaulets of a senior lieutenant and the sleeve insignia of a captain third rank (lieutenant-commander). The third officer wears the epaulets of a captain second rank and the sleeve insignia of a captain third rank.
Continuity mistake: The submarine surfaces among icebergs at the end. Just as the others go back into the submarine, the Doctor stays up there. Some snow goes onto his lip and his hair. In the following shot, we can see he isn't moving. But in the next shot, the snow on his hair and lip isn't there anymore.