In his latest newsletter, Michael Quinion tells us that a couple of his readers "spotted a headline error that turns up on US newspaper sites so often that it has become a perennial joke. Let’s give it one last moment in the sun because this time it appeared (on 26 January) on the website of the prestigious New York Times: “Police Officer Shoots Man With Knife in Lower Manhattan”. The NYT rapidly changed it."
The problem is that this isn't an "error", it's merely structural ambiguity that is fully grammatical and permitted. And not one that anyone really misunderstands it. Sure, "police shoot man with sniper rifle" is somewhat rude to your readers, though I expect the readership would be able to understand from context who had the rifle.
But "police shoot man with knife"? Really? Do people think it's a knife that fires bullets, or a gun that fires knives? "Police shoot man with black hair" - still an "error"?
Look, I'm not saying that the sentence is flawless. Writing things that make your readers drop out of the text to laugh (unless it's a comedy piece) isn't good writing; it might even be slightly rude. But it's not a grammatical or syntactic error.