The couplings between cars shown on the train in the American west were the buffer-and-chain type, which are used in Europe and were never used in the United States. In 1872, when the story takes place, link and pin couplings were used in the US.
When crossing the Atlantic on the steamship, it was originally bound for Bordeaux. When the captain is locked up, Fogg instructs the crew to head for Liverpool. However, he would have been much better off aiming for Southampton as it would take about the same time to reach, but he would be considerably closer to London than if he had to travel from Liverpool.
When the insane thief who has stolen the bank's money is apprehended, he is introduced by McBaines to Wentworth as believing that he is King Henry IV. However, the quotations that he screams out are from Shakespeare's Henry V, not Henry IV, namely the speech that the young king gives before the Battle of Agincourt. This could, of course, be because the man is deranged.
In the final scene, when Fogg and the Princess are getting married and kneeling at the altar, they are shown the wrong way round. The convention is, and always has been, that the bride is on the groom's left as they face the altar. Here, she is shown on Fogg's right.