Waterstone's or Waterstones?

According to BBC Breakfast this morning Waterstone's is planning on dropping its apostrophe. With this in mind they sent a reporter out to discover if people really knew what this meant and illustrated it with a board stating

Breakfast at its best
Breakfast at it's best

and asking which was correct. Quite amusing really as this isn't quite the issue at hand. As the gentleman from the English Spelling Society pointed out the first sentence is the correct one, although there was a little mumbling when he mentioned the apostrophe and being possessive.

So where's the problem with using those sentences as a demonstration regarding the Waterstone's/Waterstones story? Well in the case of "Breakfast at it's best" the apostrophe is used to indicate a contraction, the omission of the letter "i", for Waterstone's the apostrophe indicates a possession "The store belonging to Waterhouse is Waterstone's store". But who cares and why bother? Allow me to demonstrate.

Consider getting breakfast for a dog that would be "The dog's breakfast" so far so simple, but what if there's more than one dog? That would be breakfast for the dogs and thus "The dogs' breakfast". The confusion lies in that speaking either sentence yields identical results.

If the apostrophe is dropped there is no indication of whether it is a singular or plural and the full meaning of the store's name is lost "Waterstone's book store".

It's not difficult -

Are you omitting a letter? - Use an apostrophe to indicate that letter.
Are you indicating that something belongs to something/one? - Use an apostrophe.
Otherwise - Don't use an apostrophe.

If in doubt consider the sentence without omissions or replace the possessive with his/her/its to see if it still makes sense.

"Breakfast at it's best" becomes "Breakfast at it is best - incorrect.
"Dog's breakfast" becomes "His/Her/Its breakfast" - correct.