"The NSA, CIA, and FBI worked together to catch the killer."
Does this sentence seem right to you? Would you have inserted a "the" before CIA and FBI as well? These are the little things I spend time thinking about.
I had reason to rethink this construction during a job this week. Afterward, I looked it up in the Chicago Manual of Style to see what its advice was. Chicago says:
"With a series of coordinate nouns, an article may appear before each noun but is not necessary {the rose bush and hedge need trimming}. If the things named make up a single idea, an article need not be repeated {in the highest degree of dressage, the horse and rider appear to be one entity}. And if the named things are covered by one plural noun, the definite article should not be repeated {in the first and second years of college}."
So what it appears to come down to is context. In this case, the NSA, CIA, and FBI are joining together to accomplish something in aggregate. But if I wished to refer to each separately, I might use the "the" three times: I applied to the NSA, the CIA, and the FBI.
And then there's the case of distinguishing one entity from multiples. "I consulted a priest, a minister, and a rabbi" is very different from "A priest, minister, and rabbi walk into a bar." In the latter case, the lack of "a" makes it seem like it is a one person, and even if you see the plural verb "walk" afterward, you're likely to think it a mistake. It creates cognitive dissonance. It's not wrong, but it just may trip up the reader.
It's easy to write such confusing sentences, because as a writer, you already know the definition of what you're writing about. But the reader does not. As an editor, I sit in the reader's shoes and work to identify and fix those "not wrong but possibly confusing" constructions. The result is a clearer sentence and a happier readership.