Other mistake: When the pilot of the Spitfire is shown ditching into the water, his engine is windmilling at high RPM as he impacts the water. This would have resulted in all of the prop blade tips being bent backwards; however, as it shows him trying to escape the sinking airplane, the prop blades are perfectly straight.
Revealing mistake: The ship set up for the capsize scene is supposedly mid channel and heading for England when it is bombed by the Heinkel, but it is at anchor.
Factual error: The Spitfire had enough browning MG ammunition for 16 seconds, hence pilots shot in very short bursts. In the film at least 30 seconds of fire came from one aircraft.
Continuity mistake: There's a repeated issue with weather continuity throughout the movie. Many scenes cut between daylight, sunset and cloudy weather literally seconds apart. This has nothing to do with the particular time structure of the movie, since it happens between shots and reverse shots of the same scenes. These inconsistencies are particularly obvious at the opening scene, at the Stuka bombing and at the rescue of the shivering soldier. In these scenes, weather turns from heavily cloudy to fully sunny just from one shot to the next. (00:26:20)
Factual error: When told instructed by Fortis leader to stay at 500 feet to leave 40 mins of fighting time. Pilot confirms saying ".5" however for altitudes under 1000 feet "cherub" would have been used - "cherub 5" being 500 feet.
Revealing mistake: In some of the shots where multiple British soldiers are together, most have their rifles (Short Magazine Lee Enfield, No. 1 Mk 3) slung or are holding them. Some of the rifles are dummy, toy rifles that look nothing like the Enfield and are just to stand in.
Factual error: When Commander Boulton is looking out to sea at the civilian navy he has the binoculars backwards.
Suggested correction: No, he doesn't. The objective lenses are smaller than on modern binoculars but he definitely has the binoculars the right way round. You can tell he has the binoculars the right way round because the objective lenses are on the outside of the two barrels. The eyepiece is on the inside of the barrels.
To add to the above correction, you can see WW2 binoculars at https://globalwarmuseum.com/produkt/binoculars-british-army-1943-mk-iii-x6-taylor-hobson-perfect-optics/. Commander Boulton can be seen holding them correctly at https://fyeahkennethbranagh.tumblr.com/post/168344257844/dunkirk-2017-dir-christopher-nolan.
Factual error: The Heinkel He 111 defensive rear gun sounds are ridiculously low and slow (pom pom pom). In reality fire rate of the 7.92mm and 13mm guns was much faster.
Continuity mistake: When the two British soldiers are exchanging a bottle of wine, it's full in one shot but when given to the other soldier it's suddenly less so.
Continuity mistake: During the spitfire scenes over the channel, it's day light, however, when one of the ships was bombed and the soldiers jump over board, it's pitch black. Several cuts between these scenes each time show daylight in one and night in the other.
Other mistake: When Tommy walks down the stairs on the boat to be bombed, one of the soldiers in the top middle of the left side of the screen can be seen pretending to eat a sandwich by repeatedly snapping his teeth near the edge of the crust. (00:31:15)
Visible crew/equipment: Towards the end of the movie when Farrier is watching his airplane burning on the beach, a camera crane can be seen from a distance getting in the frame on the right side of the screen. (01:38:40)
Continuity mistake: At the start the damage to the wooden gates changes between shots. (00:02:10)
