Factual error: When the returned soldiers are on the train at the end of the film, it's an open plan post-war British Rail Mark I type, which where built from around 1950. Also the blue upholstery on the seats looks to be the corporate blue introduced by British Rail in the 1960s, used by the preserved railway owning the stock, and not what would have featured in Southern Railway carriages of the time. The carriages also have horizontally-sliding windows, which are far more contemporary than wartime trains, which had windows with a much larger vertical opening, held in place by a leather strap.
Factual error: When the boat returns to England they state the cliffs are Dorset. There were 3 evacuation routes from Dunkirk - all to Kent. It would be nonsense to sail from Dunkirk to Dorset as you have to almost pass Dover on the way! (never mind the fact the boat would probably not have made it without refuelling).
Factual error: When asked whether he had a gun, Cillian Murphy says he had a .303. As an officer, he would have carried a pistol but not a rifle. It was not until later in the war that British officers began to carry weapons other than sidearms, and even then it was usually SMGs and not rifles.
Factual error: As the last Spitfire runs out of fuel, it continues to fly along the beach; then apparently turns around and flies the opposite direction along the beach still maintaining his steady low altitude. This is an impossible feat as distance flown (and any turn without power) results in loss of altitude.
Factual error: Generally the clothes are not 100% of WWII. We see a lot of hats and head protection which didn't exist at that time. Also the holsters for the side guns were all closed and not open like in the movie.
Factual error: Colonel Winnant wears a regimental cap badge. In fact, full colonels (as he is) and brigadiers have a different cap badge (a lion standing on a crown). It's not entirely beyond the realms of possibility that he would choose to continue to wear his old cap badge, but it would be very unusual (and completely against regulations).