German paratroops did not land via parachute in North Africa until late 1942. The fall of Tobruk was in summer 1942. Also, the German paratroopers are shown descending with a kit bag attached by a line to one leg. This was a British and American technique, not used by the Germans.
After the plane crash when Katharine has been moved to the cave, Laszlo leaves her with some supplies to hold her over until he can return with help. When Katharine is having problems with a flashlight, she smacks the light against her palm and looks into the light's reflector. The bulb shown in this shot is a halogen high-performance type lamp which was not available until 1959 (in A.C./household bulbs. These bulbs were not available for flashlight use until the late 1970's/early 1980's when longer lasting alkaline batteries were available to supply these extremely bright and power thirsty bulbs.
Katherine's husband has taken off to take pictures for the British Army because, "They want maps of all North Africa, That's why he is in Ethiopia." Ethiopia is located in Eastern Africa, not in North Africa.
As Hana reads the note Almásy has written on the Christmas cracker paper - "the heart is an organ of fire" - we see that it is dated only "December 22". However, when we see Almásy originally writing the note in flashback, we see him date it "December 22nd 1938".
Kip is buttoning his shirt from the top down as he darts past Hana while leaving the barn. When he turns to face her a moment later, the buttons he buttoned are unbuttoned and two lower buttons are buttoned.
In the first scene with the plane flying over sand dunes: the shadow of the wing on the plane, the shadow of the plane on the dunes, and the shadows cast by the dunes themselves suggest three different positions for the sun. The shadows of the dunes also change length and direction when the camera angle changes to behind the plane in the next shot.