The Times obituary of William Zinsser, the author of On Writing Well, includes this sentence: "In his late '80s he wrote a blog on popular culture, the craft of writing and the arts for the website of The American Scholar that won a National Magazine Award for digital commentary."
It's a small thing, but there's no need for the apostrophe before "80s." One might use an apostrophe to refer to the decade the 1980s — the apostrophe in '80s would stand in for the missing digits 19. But referring to someone's age, there are no missing digits. So there should be no apostrophe.
There used to be copy editors at the Times who would care about getting this sort of thing correct, especially in, of all places, an obituary of the author of a book on writing well. Or at least there would be Times readers who would catch it and write in so the paper could fix it for online, or editors who would catch it and fix it in later editions. But the many rounds of buyouts and layoffs at the Times that have reduced the level of experience to the point where it has started to affect quality adversely. That quality has already been reduced in the first place by the decline in American education when it comes to grammar, punctuation, and usage.