(At 2:10) The escaped prisoner is being chased by a German soldier on a motorcycle. Up to the point that he drives into the field, his motorcycle has a rear seat and rear fender that wraps down. After entering the field, he's driving a different motorcycle: it's essentially a motocross bike.
(At 8 min) When the British fighter strafes the German vehicles on the bridge, the bullet explosions run along the length of the bridge even though the fighter flies in perpendicularly to the bridge.
In this movie, the Stalag Luft III Commandant von Lindeiner-Wildau is taken to Berlin and shot. In actuality, he feigned mental illness to avoid imprisonment and was later wounded by Soviet troops. He surrendered to the British, was sent to a POW Camp in England, and repatriated in 1947. He died in 1963, aged 82.
In reality, the executions (which were known as "The Stalag Luft III Murders") were investigated solely by the British Royal Air Force's Special Investigations Branch, headed by Wing Commander Wilfred Bowes. The detachment of 19 Officers and NCOs were active for three years, and identified 72 men as guilty of either murder or conspiracy to murder, of whom 69 were accounted for. Of these, 21 were eventually tried and executed (some of these for other than the Stalag Luft III murders); 17 were tried and imprisoned; 11 had committed suicide; seven were not traced, although four of these were presumed dead; six had been killed during the war; five were arrested but not charged; one was arrested but not charged so he could be used as a material witness; three were charged but either acquitted or had the sentence quashed on review; and one remained in refuge in East Germany. They were aided greatly by Germany's meticulous record-keeping.
At 46 minutes into Part 2, Corey makes reference to The Cold War. It's 1945, and while The Cold War was in its embryonic stage, it wasn't referred to as such until years later.