The Letter - S5-E7
Factual error: Sgt. Saunders is looking at a color photo of his kid brother in a letter from home. Aside from being prohibitively expensive for the average family to afford, color photos were not common. Also, the wartime rationing of photo chemicals for color film used by civilians would not be available.
The Losers - S5-E2
Factual error: As Sgt. Saunders and his squad dodge artillery fire in the ruined city, modern high-tension electrical towers are shown. Also, no electrical towers whatsoever would have survived a prolonged artillery bombardment without being damaged or destroyed.
Factual error: McCall shoots a German ten times with his M1. But the M1 could hold only eight bullets.