Factual error: The underground station shown is not St. James Park, which would be 1 stop east on the district line. St. James Park has green and yellow tiles on the wall indicating District and Circle lines. The platform in the film has black and brown tiles, indicating Northern and Bakerloo lines.
Continuity mistake: When Churchill is delivering his first speech on May 13th, Neville Chamberlain places a handkerchief on his leg to use as a signal to his fellow MPs. During the speech you can see Chamberlain sitting a few places away from Churchill but the handkerchief is missing. Then, a short while later in the same scene, the handkerchief is back with Chamberlain's hand over it.
Factual error: Churchill's ride on the Underground to Westminster (disregarding whether or not it happened) would have been on either the District or Circle line, both of which, being sub-surface lines, use larger rolling stock. The action took place on a much smaller "tube" type train.