As the corporal is flipping through the sequential stack of Axis Sally broadcast recordings, the dates shown are "6/8/43", "6/9/42", "6/10/43", "6/12/42", and 6/12/43"
When the enemy agent retrieves their handgun and later produces it, it is a German Walther P-38/HP Double Action Pistol. In the middle of the next to final scene, without the agent having switched guns or removing it from the hand, the agent is instead holding a German Luger P-08 Single Action Pistol, a totally different gun from a different era.
There was no Friday the 13th in June during America's involvement in World War II.
The episode takes place in 1943. As General Savage tears the page off his desk calendar, we see the date go from Friday, June 13 to Saturday, June 14. June 13th was a Sunday in 1943.