The 45th Infantry Division used a red square with a yellow swastika as their division's emblem starting in 1924. Swastikas were a common Native American symbol, and the 45th was/is based in Oklahoma so it was a tribute to the Native Americans who lived there. Because the German National Socialist party also used the swastika, the 45th had to change their emblem in 1939 to the yellow Thunderbird it has used since.
The SS troops faced in the Vosges were units of the SS Nord Divsion, who'd spent the greater part of the war in Finland on the northernmost reaches of the Eastern front. When the Finns surrendered, they retreated across Finland into Norway, They were supposed to take part in the Battle of the Bulge, but were too long in refitting after getting shipped back to Denmark. They took part in Operation Northwind, a futile offensive into the Vosges mountains in eastern France in the early weeks of 1945. The unit had a reputation of being particularly prone to collapse of morale and suffering routes, which they had done twice during their tour of duty in Finland.
The grips on Capt Sparks' pistol are known as "Sweetheart grips" and were common during the war. Soldiers made them from the Perspex windows of shot down aircraft specifically to put pictures of their sweethearts under as a good luck charm.
Major General Robert Frederick who is shown as the commanding General of the 45th Infantry Division, was only 37 when he was promoted to Major General. He along with Major General James Gavin who commanded the 82nd Airborne Division were the youngest two star Generals in World War 2. They are nine days different in age. MG Gavin was promoted in November 1944, and MG Frederick was promoted I. December 1944 General Frederick previously commanded the 1st Special Service Force which was a group of Canadian and American soldiers who were dramatized in the movie The Devil's Brigade starring William Holden as then Lieutenant Colonel/Colonel Frederick. Frederick was awarded two Distinguished Service Crosses for his action while operation with that unit.
Throughout the series the American vehicles, especially the trucks, are shown with bright red signal and marker lights like typical, contemporary, civilian vehicles. This is an error as during the war these trucks would only have small, barely visible, marker lights and they wouldn't be used anywhere near the front lines as orders would dictate using blackout drive at all times.