General Reinhardt's and Captain Blackburn's dress uniforms have several awards/ribbons in the incorrect precedence: the Purple Heart does not take precedence over the Distinguished Service Medal or the Bronze Heart.
In an early scene, a US Army captain addresses a US Army master sergeant as "Master Guns", which is how a USMC master gunnery sergeant would be addressed. No one in the Army would ever make that mistake.
A US Army captain is told about Operation Valkyrie before it occurred, but the Allies didn't know about Valkyrie until after it failed.
A US Army major general addresses a US Army master sergeant as 'Gunny', which is how a USMC gunnery sergeant is addressed.
While hanging from his parachute rigging, a US Army soldier opens a flick knife (switchblade) with both hands.
Very early in the movie, when the Sturmbannführer SS officer leaves his car, there is a German soldier on guard duty not wearing his helmet properly. He has it pushed back on head which would never be allowed. He also looks like he could use a haircut,
When the Allied group is in the bunker, it is attacked by a squad of Germans including a tank. When they exit through the escape hatch and fight the remaining Germans outside the bunker, there is no tank to be seen. The tank would have made it essentially impossible to escape.