My pet peeve is apostrophes on plurals. That one just grates on me.
OOOOOOOOH! That's a good one!
Worse than sticking them before a final "s" to make plurals is attaching apostrophes into present-tense singular verbs, presumably to make them more understandable to the (presumed equally illiterate) reader.
Examples abound on the Web, and on this very forum.
Also, much more common -- so common that it must be taught as correct in public schools these days -- is the misuse of the apostrophe in trying to make a pronoun possessive.
Don't people realize that the pronouns "hers" and "its" are already possessive case and require nothing more? We see "her's" from time to time and tend to disregard it as a typo or careless spelling.
But the apostrophe in "it's" has legitimate use to designate a contraction: it is. When someone writes, referring to the MSM for instance, "it's leftist slant that I can't stand," the literate reader thinks the sentence is over . . and then we get hit with another clause like, "is what's killing the network news." A complete sentence? You decide. Overly complete, IMHO, since there's two verbs.
Good writing does not leave the reader wondering what the writer was trying to get across.