One source of confusion when writing things like "the 1920s" v. "the '20s" is that in one case the apostrophe replaces an omitted part. While I can see that it might be acceptable to write "the 1920's," (though the apostrophe seems unnecessary) or "the 1920s" or "the '20s," I often see "the 20's" -- which seems clearly wrong, since that form omits the apostrophe that would actually convey a meaning, but uses one that adds none.

LOL