At the start a newsreel is shown describing the allied build-up to combat Germany's Africa Corps and "looking forward to wiping the smile off General Rommel's face". All of this took place in 1942; however the newsreel is prominently dated 1944. Rommel even left Africa on 9 March 1943 and never returned. Newsreels during WWII were up to date with their information, not two years late.
Fully fueled an M3 tank had a range of 121 miles, in this movie they drive a lot more than that.
When the tank is being attacked by a German aircraft, the plane is a Fiat G.59, which is an iconic Italian model of fighter plane.
Capt. Halliday's "pips" are not British. They are most likely German Officers Pips.
The M3 tank used in the movie was painted in a desert sand color. US forces used OD Green. While other forces used sand color and camouflage colors. The movie did show the tank crew in OD Green clothing which would have been correct.
When Gunn runs up to the downed (and armed) German pilot, he has his .45 auto out and orders the pilot to surrender. Then after a brief chat, Gunn then cocks the .45 indicating the pistol was never ready to fire during the threat.
When the Americans and British run up on the downed German pilot, not only has Belushi drawn on the German with a non cocked pistol, but the Sudanese soldier has also approached the German without a round in his SMLE rifle. After shouting at the German to drop his pistol, Belushi cocks his pistol, and the Sudanese works the action on his SMLE, both putting a round into their weapon's chambers. Neither soldier would have approached an enemy combatant with weapons that did not have rounds in their chambers, and therefore unable to fire.
Capt. Halliday's cap badge is post 1953. It features the crown brought in after the accession of Queen Elizabeth II.
Captain Halliday tells Sgt. Gunn that the Qattara Depression is the worst place in Libya. The Qattara Depression is actually in northwestern Egypt.
The US Army never fought in the Sahara Desert or in Egypt or Libya. US forces fought from its beach heads in French Morocco east towards Tunisia; where they linked up with the UK & Commonwealth forces coming west from Egypt. So geographically the US fought in the coastal zone of North Africa, while dry is not a true desert.