My view on the classic prescriptive bugaboo known as dangling modifiers or dangling participles (henceforth, danglers) is, I think, a bit unusual. I don't regard danglers as grammatical mistakes; that is, I think the syntax of English does not block them. Yet I do think they constitute mistakes, in a broader sense, so in a way I am with the prescriptivists on this one. A dangler is an error in a domain that I have compared (for want of a better way to put it) to courtesy or manners. I regard danglers as minor offenses against communicational etiquette, but not against grammar. The argument against danglers being grammar errors is simple: they are too common in even careful published writing, and come too fluently to the keyboards of even excellent writers, and are accepted without remark by too many educated readers. If you ask what evidence there is that, for example, verbs come before objects in English, the answer is that it is overwhelmingly clear from just about all of everybody's usage just about all the time, and from the blank "What's gone wrong with you?" reactions if you try putting the object before the verb. The evidence on danglers goes entirely the other way. Here, for example, is an example in the carefully edited prose of The Economist (October 3rd, 2009, p. 79):
A report to the British House of Commons this year highlighted the case of an elderly British citizen called Derek Bond, who was arrested, at gunpoint, in February 2003 while on holiday in South Africa. After being held for three weeks, it turned out that the American extradition request was based on a fraudster who had stolen Mr Bond's identity.
The only relevant thing the syntax says, I believe, is that subjectless non-finite clauses, and preposition phrases having such clauses as complement of the preposition, and predicative constituents such as adjective phrases, may be used as adjuncts.
And all the semantics says is that the target of predication in such cases is filled in by reference to a grammatically salient noun phrase (NP) in the immediate vicinity. That's it.
Consider in this light the task of interpreting the second sentence in the quotation above. After what? Somebody being held for three weeks. Who was held? We're guessing thus far, so let's wait and see what the subject of the matrix clause is… Hmm, the pronoun it. That's not very promising: what non-human could have been held? Let's go on. It turned out that… This makes it clear that the it was a dummy — a meaningless placeholder in a context where a complement clause is in extraposition (postponed till the end of the clause containing it). Well, what's the subject of the clause in extraposition? The American extradition request. But surely that is not what was held. Let's go on. Was based on a fraudster… Could the target of predication be a fraudster? No, that makes no sense. Any other NPs? Well, there is one more (though we're down to NPs that could hardly be called grammatically salient now): the object of stolen, namely, Mr Bond's identity. But that doesn't make sense either: this isn't about the South Africans holding the man's identity.
Wait a minute, though: if we look inside that NP we see that its determiner is the genitive NP Mr Bond's. Perhaps the thing to do is to ignore the genitive case on that and try Mr Bond as the target of predication. After Mr Bond had been held for three weeks. Yes, that would make sense. We'd better assume that.
You can get there. But what a struggle. Floundering around for what could be as much as an extra second, which in language processing is a very long time, there were four different false leads planted in the text for us to pursue — four NPs that were not the right choice for the target of predication we needed to plug together with the being held clause.
It is true that if we had looked back at the previous sentence instead of plowing on we would have noticed that there was an indefinite NP, an elderly British citizen called Derek Bond, which was a prime candidate. If we had happened to be still holding onto that, and we had tried plugging in a definite version of that ("the aforesaid elderly British citizen called Derek Bond"), it would have worked like a charm. But that NP was embedded in a larger one (the case of an elderly British citizen called Derek Bond), and following it we had read four other NPs (gunpoint; February 2003; holiday; and South Africa. Any syntactic salience that NP might have had was lost before we began the next sentence.
Hearers and readers can't be expected hold onto every NP they run across, keeping all of them live and active in short-term syntactic memory just in case perhaps one of them might be suddenly needed to make a subjectless clause adjunct interpretable. That's not how we work, or so it seems to me. Mostly we expect the sentences we encounter to be parsable independently: take any one of them on its own and you should be able to understand it down to the level where all that remains is assigning antecedents to pronouns and filling in gaps due to ellipsis. And that second sentence does not meet the condition. We had to fumble around and look all over the place to find a target of predication for the subjectless clause in the initial PP.
That's a shortcoming on the part of the writer. Not a disastrous blunder or a major display of ignorance; just a minor discourtesy to the reader. That's what I think danglers are.
But they are extraordinarily common, and they occur now and then even in what is in general terms excellent writing. The more sensitive to syntax you are, the more you will be struck by them and incommoded by them. The more you exercise your common sense rather than your syntactic sense when figuring out what a subjectless non-finite clause adjunct must mean, the less you will notice them. But they will be out there, in everything you read (somewhat less frequently in conversation because of its lower syntactic complexity — we don't use non-finite clause adjuncts so much when chatting about who's going to pick up the milk).
Just for fun (but not out of a lack of courtesy) I embedded a deliberate dangler in the paragraphs above. Now you will know how careful a reader you are. If you didn't notice it, that underlines my point that you probably do not operate by a set of syntactical rules that forbid danglers. And if you did notice it, and experienced that odd extra second of squirming around looking for a target of predication, then you'll know what I've been talking about.