Question: How is it possible for everybody from other countries to know about the wager that Phileas made when the only ones who knew about were the members of the Academy of Science?
Question: When Passepartout, Phileas Fogg and Monique are looking at a map to find a way of avoiding the British police, Phileas notes that they can't go to Singapore or Hong Kong because they're both British Colonies. Monique asks if England owns every country in Asia, Passepartout says they don't own China. Since Hong Kong is located in China, shouldn't England own that as well?
Answer: Hong Kong was indeed under British rule from 1841-1997. In short, it stems from the First Opium War where in the aftermath of the war, China ceded (gave up control of) Hong Kong to the British. After the war, with the cession of Hong Hong, it wasn't technically part of China any more and Britain didn't really seek to occupy more of China.
Question: Queen Victoria made Phileas realize that he won the wager because it was still day 79. If she knew that Phileas arrived a day early, how come everybody else in London, including Lord Kelvin, thought it was actually day 80 and that he lost the wager when the tower bells began to ring?
Answer: In reality, it would be impossible that so many people would make this mistake. However, it serves the movie's plot for the error to be discovered by one person at the last moment because it provides an unexpected upset to a perceived outcome. In this case, it was by Queen Victoria, which added an additional twist.
Question: Is there any reason why Passe-partout and the Wright Brothers don't appear together? Were the filmmakers afraid people would get confused and think they were watching "Shanghai Noon"?
Answer: Might be. But most unlikely. Many actors who have played in the same movies often "bump" into eachother in other movies as well. The most reasonable explanation that Passepartout doesn't meet up with the Wright Brothers is that his character is not needed in the scene between Fogg and the Wright Brothers.
Question: Why did Inspector Fix take sides with Fogg at the end of the film?
Answer: He felt foolish for accusing Fogg and hounding him across the world, the least he could do is help him win the wager.
Not only that but, like Lord Kelvin's other associates, Inspector Fix was berated constantly by Lord Kelvin and was even thrown out of a window. Inspector Fix had got tired of Lord Kelvin's bullying and decided to tell the truth in front of everybody.
Answer: In order to stop Fogg from completing the journey, his rivals at the Academy wired (telegraphed) details to confederates in the countries he visited with instructions to waylay him.