Referring to "the 50's" or "the 60's" is grammatically incorrect

Contractions for numbers follow the same rules as contractions for words. As a apostrophe goes where the letters are dropped in a contracted word (e.g. you are into you're) the same applies to numbers (e.g. 1950s into '50s)... By putting an apostrophe between the numbers and the "s" (e.g. 50's), you are making the "s" possessive. 

I see this type of mistake ("music of the 60's") frequently while browsing the web - and sometimes in the comments here.  I think I sometimes refer to groups of years as "the 90s" without an apostrophe at all - not sure if that's acceptable.