Is an apostrophe with a decade (e.g. 1920’s) generally considered “incorrect”?

I typically don’t use an apostrophe with plurals in any situation, but I always assumed that the use of an apostrophe in constructions like acronyms:

Forty BA’s were given out to students this year.

or numbers:

Though the greatest period instability occurred during the 1950’s when. . . .

was more or less ok. I would personally use BAs and 1950s here, but I've never thought the apostrophe in this case was necessarily “incorrect”. What say ye?

My answer focuses on the header question about decades—which is the question that most readers will probably expect to find answers to here. With regard to decades expressed in numerals rather than spelled out in letters, some style guides recommend omitting an apostrophe, while others recommend including it. For example, from The Chicago Manual of Style, fifteenth edition (2003):

9.37 Decades. Decades are either spelled out (as long as the century is clear) and lowercased or expressed in numerals. No apostrophe appears between the year and the s.

^{the nineties}

^{the 1980s and 1990s (or, less formally, the 1980s and '90s)}

The Associated Press Stylebook (2002) adopts a rule very similar to Chicago's:

decades Use Arabic figures to indicate decades of history. Use an apostrophe to indicate numerals that are left out; show plural by adding the letter s: the 1890s, the '90s, the Gay '90s, the 1920s, the mid-1930s.

The Oxford Guide to Style (2002), while differing with Chicago and AP on capitalizing the spelled-out decade name (Oxford University Press prefers this) and on using abbreviations like '60s (OUP condemns this), agrees with Chicago that the plural numeral form should be spelled without an apostrophe before the s:

To denote simple ten-year spans OUP style prefers, for example, 1920s or 1960s to nineteen-twenties or nineteen-sixties. To denote decades of a specific character (say, the Roaring Twenties, the Swinging Sixties) OUP prefers Twenties or Sixties to '20s or '60s.

But Words into Type, third edition (1974) takes the opposing view:

In referring to decades, the sixties or the 1960's is generally preferred (not '60's, '60s, 60's, or 60s; the last form is used occasionally for ages of persons).

The New York Times Manual of Style and Usage (1999) agrees with Words into Type about the apostrophe, although about little else:

decades should usually be given in numerals: the 1990's; the mid-1970's; the 90's. But when a decade begins a sentence it must be spelled out. [example omitted]; often that is reason enough to recast the sentence.

Clearly the question of how to render a particular decade in print is a style issue on which reasonable style guides may differ. Follow the one you have to follow, or choose the one you like.

Not an easy question. With dates, the rule is simple: no apostrophes. It's "1960s" and so forth.

The apostrophe is needed when it serves to avoid confusion: She earned all A's and B's.

The style sheet I received when I was working on texts for publishers suggested 1920s, but did not claim that 1920's was incorrect. Writers need to be aware that all magazines, newspapers, and publishers have their own style sheet for many of these questions and that there is no unanimity among them. BTW, the answer above that 20's is correct because the apostrophe indicates something missing as in a contraction is incorrect. One of the reasons apostrophe use is so confusing is because using 's to indicate the plural form of things like decades, or grades on report cards has always been acceptable. It is this rule that confuses writers who then incorrectly use the 's for plurals such as apple's and other nouns such as family names (the Smith's). It is to avoid this error that style sheets recommend the lower case s as the plural for I received 4 Bs on my report card, but if I am an A student, it is context that explains that As stands for grades not the comparison.

Best solution in such situations--find an alternative. Write the Roaring Twenties.