When we first see Peter, much is made of the fact that he has two right hands. But in a later scene, his left hand is back to normal.
After Las Vegas joke Brian has no mustache and it appears back in next shot.
In 1896 Stewie could not have had Oscar Wilde in his flat because Wilde was serving a two-year prison sentence at that time on the charge of "Gross Indecency".
When Stewie lists countries that are part of the British empire, he lists countries that didn't exist at the time.
When Stevie and Brian (Holmes and Watson) arrive in Paris via the train, they are clearly arriving at the station Gare d'Orsay, now known as the Musée d'Orsay. The show takes place in 1896, however the Gare d'Orsay was not completed until 1900.