The German night fighter lets out the iconic sound of 'Jericho trumpet' used in Stuka dive bombers. The night fighter isn't a Stuka, so it shouldn't make the sound and also the siren makes a diving airplane sound in level flight.
The movie indicates that there were three BIGOTs participating in the operation Tiger, while in reality there were as much as ten. Aboard the landing craft the other soldier says that it is like the real thing, to which Kelso answers "yeah, except for the bombs and the gunfire, blood, random dead body..." They should've known that the exercise included live rounds and artillery to acclimatize troops to real battlefield conditions. In fact, the real landing included an incident where some of the troops landed too early and were hit by the artillery, losing hundreds of men to friendly fire - more than in the actual landing.
In the firing range Martineau picks up a gun saying it is a Walther PPK. It is actually a Walther P38.
When Rommel is inspecting the troops there are Soviet T-34/85 tanks in the background. These tanks can also be seen later in a convoy.
Harry, as Vogel, says to Hauptsturmführer Müller : "I will make my report to Herr Himmler . . . " referring to Reichsführer-SS Heinrich Himmler. In German, however, this would be : "Ich werde Herrn Himmler Bericht erstatten . . . ", and thus, it should be Herrn Himmler, not Herr Himmler, because this is the dative case in German, where something is given to someone.
The plane used in the flight to France is a postwar civilian model and certainly not the Westland Lysander that was used for the trip in the original book.
The aircraft in which Rommel's double arrives at Jersey is not a contemporary aircraft nor German. It is likely a post-war American Cessna.
There are several scenes where you can see a vast mountain range in the background, there is no such scenery on Jersey Island. Also in these scenes you can see Autumn leaves on the trees. It's supposed to be April and spring should be in full bloom as late April in 1944 was unusually warm. Despite this, everyone is wearing thick overcoats.
Harry is supposed to be a British agent, but has a thick American accent.
Field Marshal Erwin Rommel is shown smoking in the film. The real Rommel was a well-known teetotal non-smoker.