OK, the fact that Mario
is German puts things in a new light. To answer the fundamental question, yes, I think that you see this differently because you're German. What I don't see is how somebody can laugh at Hogan's Heroes
, but take this one humorous line so seriously. As others have pointed out, there's always room for a little comic relief in "serious" episodes. And honestly, you might feel differently because of the subject matter, but this isn't an unusually serious episode of Trek in its tone or approach. Trek is just an adventure show at heart, and putting the crew on the "Nazi planet" wouldn't have been treated any more "somber and grave" than putting them on the "Roman planet" or the "post-apocalyptic America" planet.
To offer a better American parallel than the slave trader example...try altering the scenario to one where Kirk is disguising himself as a member of the Ku Klux Klan. If Spock had told Kirk he made a convincing Klansman, I think that would have been seen as tasteless and offensive by many Americans.