Continuity mistake: Newkirk comes out of Klink's office with a code book, and passes it to Le Beau, who immediately holds it up and opens it. In the close up, Carter's hands bring up a book with a camera in it, and Le Beau brings the book out from his back and opens it again.
Factual error: In this episode, the HofBrau (which should correctly be written "Hofbräu") is displaying a big red neon sign above its door. From 1939 on, air raid regulations throughout Germany strictly prohibited any unnecessary display of light at night. Any light visible from more than 500m away was considered a breach of air raid regulations.
Factual error: In the restaurant in Hammelburg, where Schultz discovers Hogan and Newkirk, there's an advertisement for "Brauerei der Jager, Stadt Wien." (Wien = Vienna) Vienna and Hammelburg are more than 500km apart, and if Hammelburg were near Düsseldorf, where the series puts it, it would be more like 700km. That's a bit far away for a brewery to advertise in the pre-globalisation era.
Factual error: General Kamler awards Schultz what he calls "The Iron Cross Fourth Grade." There never was a version of the Iron cross called that. The Iron cross came in two ranks, called 2nd class ("zweiter Klasse") and 1st class ("erster Klasse"). The ranks higher than that were called the Knight's Cross ("Ritterkreuz des Eisernen Kreuzes") and were never pinned to the chest but worn around the neck.
Factual error: Schulz repeatedly calls Klink's adjutant "Kapitän." In the German armed forces the rank Kapitän only exists in the Navy, the German equivalent for the American rank of Captain (which is obviously meant here) is Hauptmann or Stabshauptmann.
Continuity mistake: As Schultz is going to get checked out, Hogan and the boys stop him, and Hogan feels Schultz's neck. Schultz's arms are by his sides, then after the angle change, they're by his hips. Also, there's two men walking behind the group that weren't there a second before.