In this episode as well as the following, we see Nazi command banners in the form of a black eagle on a red background or a black swastika surrounded by gilt leaf on a red background.
Either the holodeck has very poor records or the set decorators had never studied their history, as both are incorrect. The standard for command was a gold eagle clutching the swastika in it's claws, usually with the swastika surrounded by a white circle. The eagle
on a solid background was the standard of the Weimar republic and the background itself was white, not red. If a swastika-only flag was displayed at command or otherwise anywhere else in Nazi Germany it was contained in the aforementioned white circle.
One of the vehicles shown in the WWII street scenes is a Citroen 2CV. This car was not developed until just after the war and the one shown is actualy a 1980's special edition 'Charleston' model!
All of the German soldiers in this episode are elite SS troops - historically, the majority of them would be the more common Wehrmacht.
Bakeries and other shops are shown as being open on a Sunday, which wouldn't happen in France in the 1940s.