Oh Bags, these threads have made me paranoid I'm ok with the 'if a word is missing' apostrophe, but the possessive plural/single one throws me into confusion!
Surely it depends how many fathers you are talking about.
The US government has stated that Father's/Mother's etc is correct because it is a day for each person to celebrate just one person. All the commercial cards I have seen say Father's ....just one Father each!
But when writing about the Day as a day for all Fathers it would be Fathers' Day
There is also the argument that as Fathers do not own the day it should have no apostrophe.....