My father remarried last October and his wife's passport is still in her old name. They will be going on a cruise this October and asked my advice about getting the name changed on her passport. I advised to leave it as is. Most cruises don't ask for any other ID and their tickets were purchased in their original names.

Am I correct in believing they would have no difficulty on their cruise?

As for flying which they never have done and are unlikely to do in the near future, would carrying the certified copy of the marriage certificate be enough? Her passport is not up for renewal till 2015. What future problems might they be heading for if they do not update her passport to her married name?