In the section of the movie set in 1935, there is a scene where Robbie is daydreaming and the image of a four engined bomber crosses the screen. The plane is in fact an Avro Lancaster, which entered service in 1942.
When Robbie is standing behind the movie screen at Dunkirk, the men in the audience hum/sing "White Cliffs of Dover." The song was written in 1941, and Dunkirk Evacuation was in 1940. The song became most famous when Vera Lynn recorded it in 1942.
When Robbie and his two comrades pass through a bombed-out factory complex on their way to Dunkirk, they stumble along a Railway track where the rails are fastened Down with 'Pandrol' clips invented in 1957.
When Cecilia and Robbie are in the restaurant drinking tea, Robbie has a full cup. Then the camera moves. When the camera goes back to him and he starts to drink the tea, there is no tea in the cup at all.
In the lake scene at the manor house, Cecilia is lying on her back on the springboard with her left leg over her right in the first shot.
When the shot changes to a closer one with her feet towards the camera, she has her right leg over her left.
The birthmark under Briony's right eye is too close the the nose on the portrayal of Briony at 18 years old, compared to the other two ages. It also looks way too raised compared to that of her at 13 and 77 (which could understandably fade in later life).
In the scene when Robbie types the letter, he starts it with "In my dreams" and then presses return and starts a NEW line with "I kiss your c**t..." But later when Briony opens the letter after the rape has occurred, the first line in the letter is "In my dreams I". The second line then starts "kiss your c**t, your sweet wet c**t."
In the scene where Robbie types his "In my dreams" letter, he finishes the letter placing the period only a little ways from the edge of the paper. But when he removes the letter from the typewriter and goes to fold it, the words and period are closer to the center of the paper.
The last day of Dunkirk evacuation was the 4th of June, not the 1st. The Navy officer tells Robbie that there were 300,000 men waiting on the beach, but the 1st of June, there were about 118,000 soldiers waiting.
As the film opens, "England 1935" is displayed. When Robbie is in France, "Four years later" is displayed, which would mean 1939. But the retreat to Dunkirk, during which the scene took place, was in the second half of May 1940, which would be nearly 5 years later.
While in London, Cecilia drops a letter in the mailbox addressed to PTE Turner, 'A' Company, 1st Battalion, Royal Sussex Regiment, B.E.F. France. According to at least one source, 1st Battalion, Royal Sussex Regiment was never in France. They were in Egypt and thus, would not have taken part in the Dunkirk Evacuation. 2nd Battalion was at Dunkirk, not 1st Battalion.
Any apparent continuity errors in the fountain scene - the position of the vase, the tennis shoes, Robbie's sitting position, Cecilia's strap slip, the buttons on her blouse etc. - are not what they seem: we are seeing the same event in different ways through different pairs of eyes.
As the three soldiers are walking back to the coast, three war planes are reflected in the stream next to them ("Some poor blighter's going to catch a packet!") From that camera angle, the originals should be visible in the sky.