Drat That Apostrophe

As noted in the post below, even the Grammar Nazi enjoys a good April Fools Day joke. Especially when it drags him into a lesson on how to properly punctuate the name of the day.

Look around, and it's likely you'll see April Fools Day punctuated three ways:

• April Fools Day, as the Grammar Nazi puts it in this post and the post below.
• April Fool's Day, with the apostrophe limiting the day to the April Fool, a singular entity.
• April Fools' Day, with the apostrophe opening the holiday to fools everywhere.

Which is correct? (Hint: NOT the Grammar Nazi's way. See? I told you I still make mistakes.) But I am brave enough to correct them.

The correct punctuation is indeed April Fools' Day. So the Grammar Nazi stands corrected.