So the twist at the end is (the question title should be spoiler warning enough) that the heroes arrive in London a few minutes too late to reach the club for the deadline of the wager, so they go to Fogg's home certain that they have lost, only to learn on the next morning that they actually arrived a day early, a day they gained by passing the International Date Line while travelling eastwards.
Now while this is correct in that you would in fact gain this extra day (in exchange for all the other days of your travels being shorter), is it even remotely realistic for the travellers to be unaware of the "real" current date at that point? As I understand it, they would have had to be purely counting days since passing the International Date Line, and crossed through the USA without ever noticing that the date (and weekday!) the locals use is different from their own calendar reckoning. That seems very unlikely.
Is this adressed in the book in any way, or just glossed over to make the twist work?