When Albert and Marie arrive at the Science Academy Awards - Einstein say that he's taking the hot air balloon down - and then proceeds to pull the cord to turn on the burners - which should take the balloon up - instead it goes down.
Marie Curie was born in Poland with the maiden name Maria Sklodowska. She did not move to France until she was 24, but speaks English with a French accent, not a Polish one.
The movie is an alternate and wacky history movie. That being said, Marie Curie should not have been named Marie Curie as that is the surname of her husband in real history that she took on after marriage and not her maiden name. She was born Maria Sklodowska in Poland.
Albert's "guitar" only has four strings. That's because it's made from a violin. He is inventing the guitar by modifying a violin.
When Marie talks to Albert in the Lunatic Asylum's shower room, "If you won't do anything, who will?" is dubbed over "If you won't do anything, I will."