In the episode "Hogan gives a Birthday Party," Hogan convinces Klink to hold a fake study, citing a similar study allegedly done by another German officer proving Germans have longer thumbs. When Klink asks the point of the study, Hogan says, "I don't really know." In fact, one of the qualifications for the Aryan ideal was for the second toe to be longer than the first, so a similar study in Nazi Germany is not far fetched. Additionally, it's not uncommon for governments to fund pointless "studies" in order to, as Klink explains, "furnish scientific proof" of something already known.
An in-universe instance pops up in "Two Nazis For the Price of One," where the crew finds out that a Gestapo officer knows all about their operation. They're ordered to close down the operation and get back to London, but Hogan raises the question, "If Freitag knows about us, why weren't we arrested?"
In "Operation Hannibal", General von Behler's daughter says that there are many Germans in Germany that would like to be rid of Adolf Hitler, and would like the war to end in a negotiated peace. Unfortunately, as anyone with a knowledge of history knows, there won't be any negotiated peace, and half of Germany will be placed under the rule of another despotic government.
In the final scene, General Burkhalter's house is blown up. What if Burkhalter's wife was inside at the time, and Burkhalter blames Klink for launching the (sabotaged) rocket?
Consider how many factories, research facilities and trains Hogan's crew blew up directly, in addition to all the air bombing raids they helped plan and carry out. Now think of how many people were inside those when they were detonated. Hogan may have killed thousands of people.
Whenever Hogan is ordered to eliminate a female target (such as in "Who Stole my Copy of Mein Kampf"), rather than killing them, he sets them up to be arrested by the Gestapo. Isn't thatworse?
