In the first episode of the series, then Captain Gallagher tells General Savage that he has already lost two brothers in the war and that he is "the last shining hope in a military family," which implied he was the sole remaining son of General Gallagher. However, in this episode Colonel Gallagher meets up with his older brother Preston, so either he had three brothers and Preston is the hopeless black sheep of the family or the writers forgot they had killed off Gallagher's brothers in that first episode.
Col Gallagher's brother is in command of a joint American/Australian/British ground unit. The historical setting is the Battle of Kasserine Pass, which took place in Feb 1943. However, all Australian units were withdrawn home to defend Australia against the Japanese. The last remaining Australian unit in North Africa, the 9th Division, had been stationed 2400 km away in Egypt and in any event had departed by Jan 1943. The joint operation as depicted could never have taken place.
The part of the story regarding gasoline is an impossibility -- it presumes that Army trucks & B-17 bombers used the same fuel -- they most assuredly did not. WWII truck, Jeep, etc. low-compression engines would run on poor quality low octane gasoline, but the bomber engines required high quality / high octane aviation gasoline. If you put aviation gasoline in a truck or Jeep it wouldn't be long before you had serious engine damage. And if you put the low octane gasoline the trucks ran on in a bomber, it wouldn't even get off the ground. Plus you'd destroy the bomber's engines.
The "triangle route" shuttle missions between Britain, the Soviet Union and the Mediterranean Theater did not start until the Spring of 1944, with the Mediterranean leg terminating in Italy, not North Africa (which had been cleared of Axis forces nearly a year earlier). This story should have been set in Italy.
When the German aircraft strafe the airfield as the fuel-carrying cargo plane arrives, TSgt Komansky, whose duties include being a machine-gunner on Col Gallagher's crew, is standing right next to Gallagher. Gallagher should have let Komansky man the machine gun (which is identical to those in his turret on the plane) instead of taking it himself.