Also, it's a comedy about Jews trying to get out of Nazi-occupied Poland, made before the world knew about Hitler's Final Solution. In fact, the "Concentration Camp" nickname was probably a lot tamer til they found out what they were really for.
There's also the fact that everyone in the movie seems so certain that the end of the war will bring freedom to Poland. Notably, the 1983 version — made at a time when Poland was still behind the Iron Curtain — gives the characters a more bitterly cynical attitude about the country's prospects ("Poland, the doormat of Europe. Everybody steps on us. If it isn't the Russians, it's the Germans.")
Harsher in Hindsight: The line from the Jew's Soliloquy going "If you poison us, do we not revenge?" is a lot more powerful if you realize that the film takes place during the Holocaust.
Special Effect Failure: The shot of the horse-drawn car in the remake. You can clearly see the rope that's leading the horse.
Tough Act to Follow: Within a single film! Brooks has said he regrets opening the film with the "Sweet Georgia Brown" sequence, as the rest of the film couldn't help but be a letdown after it.