Here is an example of a bad English sentence Richard Mitchell gives in his highly readable Less Than Words Can Say (which is out of print now):
A Department of Transportation manual suggests that "If a guest becomes intoxicated," you might "take his or her car keys and send them home in a taxi."
The problem Mitchell has in mind is, I suppose, the use of "them" in the sentence (he doesn't say so explicitly in the text). Given the use of "his or her", a simple correction of the mistake is changing "them" to "him or her".
Since many people nowadays use "they" as a gender-neutral singular pronoun, they may consider the original sentence correct. The structure of the sentence, however, makes it more natural to understand the "them" to refer to "his or her car keys". In that case, even if you accept the singular use of "they", the sentence may still sound funny.