Is it a day for one mother (Mother's Day), a day for all mothers (Mothers' Day), or is it just a given day (Mothers Day)? Should the words be capitalised or does it matter if the words are in lower case?
This article, which is about Father's Day appeared this week helped make things make sense for me. I realised it is an officially declared day and thus it isn't about usage, but how the day has been declared. You'll see from the article Sonora Smart Dodd who proposed the holiday, wanted the spelling to be Fathers' Day.
My advice when wondering about terms like Mother's Day is not to wonder. Look it up in an authoritative reference such as the Macquarie or Oxford. We could argue about the correct placement of the apostrophe until we're blue in the face, so there is little point. Simply look up the word and use the accepted convention.
Now I wonder, when was Mother's Day first proposed?