I recently tried to fly from Manila (MNL) to Taipei (TPE) but at the airport ticket counter AirAsia refused to sell me a flight ticket on the grounds that my French passport was wet and that subsequently the Taiwanese immigration officers might deny me entry. The passport was in near pristine condition though (just had a few drops of water, it didn't go into the laundry or the sea), and I had no issue with other airlines just a few minutes before and after to fly to other places (namely, Ho Chi Minh City SGN and Bangkok BKK) with the same passport and same condition.
Anyway, this got me thinking: how can I know ahead of time whether the Taiwanese immigration and whichever airline I use to fly there will accept the condition in which my passport is?
Ahead of time = before going to the airport and before buying the flight ticket.