About 3/4 of the way thorough this episode Lawson has two of the diesel engines running. The subsequent dialogue makes it clear that they are still submerged and the submarine does not have a snorkel (comment about the need to vent). Operating these engines while submerged would use up all the air in the boat in seconds. Until nuclear power, the vast majority of submarines (including the one shown) operated on electric motors and batteries while submerged.
The German officer trapped with the American men in the torpedo room is wearing the dress uniform of the SS, complete with the Nazi party armband, instead on the Kriegsmarine (navy) uniform. This is extremely unlikely, as the Kriegsmarine was totally independent of the SS and, even if a SS officer was on board, he would not be wearing his dress uniform in a submarine.
In 1943, Spike uses the term "back in the day," which is a phrase that became popular through hip-hop culture in the 1990s and was not used in the 1940s.