On the other hand, this source states that:
In British usage, we do not use an apostrophe in pluralizing dates:
This research was carried out in the 1970s.
American usage, however, does put an apostrophe here:
(A) This research was carried out in the 1970's.
You should not adopt this practice unless you are specifically writing for an American audience.
This is contradicted by a forum post stating that this is simply incorrect.
Now I'm not sure anymore. Considering the sources I'm pretty sure 1960s is correct, but is there any situation, in any recognised English orthography, in which the spelling 1960's is also correct in referring to the decade (as opposed to a property of the year 1960)?