Continuity mistake: When the Stukas are shown bombing the beach, they drop a single bomb, but from beach level, you see sticks of bombs landing.
Suggested correction: The Stukas are dropping SD-2 canister bombs, a particularly nasty anti-personnel weapon. Upon release from the aircraft the bomb divided into the bomblets you see here.
First known use was bombing of England, no evidence they were used at Dunkirk. Also, the SD-2 was smaller and produced numerous small explosions. The ones we see in Dunkirk are larger and much bigger than anything the little SD-2 could ever produce - so the original criticism sticks.
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.
Continuity mistake: When the soup is about to be served, you see the horns blowing to introduce Victoria, and you can see all of the footmen lined up already with trays of soup, but in the next shot, it shows that they are just starting to march in to line up with their trays of soup. (00:10:45)
Continuity mistake: Man-seob smears some cream above his upper lip after a few smoke grenades are deployed. The amount of cream shown over his upper lip changes between shots.