In episode 2 "Day of Days", Sgt. Malarkey is seen talking to a German POW who is in the Wehrmacht and happend to grow up near where Malarkey lived. They BS with each other until Malarkey goes to catch up with the rest of Easy Company when Lt. Speirs machine-guns arond 20 Wehrmacht POW's with his Thompson.

Fast forward to episode 3 "Carentan", when Malarkey, Muck, Penkala, and Blithe are siting around talking about Speirs, it cuts to a flashback scene of Speirs executing the POW's. But instead of wearing Wehrmacht uniforms, they now have SS uniforms on....This should have been caught right away. I know alot about D-Day and Easy Company and know for a fact they didn't encounter any SS units on a large scale until a couple weeks after D-Day.