Alicia has already talked about present participial phrases and the problems of temporality they can create.
Today I'd like to look at this issue from another angle. We see frequent problems with misplaced and dangling present participial phrases, and I've come to the conclusion that these result from a misunderstanding of the structural nature of these phrases.
So let's start with a basic idea.
The Golden Rule of Modifiers
Modifiers go next to the word or words they modify.
That one might seem like a no-brainer. We instinctively write,
The brown dog ran through the sunny meadow
without ever worrying about whether to put brown or sunny in a different location. Adjectives go next to the nouns they modify. Easy peasy. Right?
Maybe. Or at least, it's easy when we're talking about single-word modifiers. Once we start getting into phrases, things become trickier.
Present participles are -ing forms of a verb which can be used
1 --in verb conjugations
The dog was running through the meadow.
(Was running is the past progressive conjugation of the verb to run.)
2 -- as gerunds (that is, nouns)
Running is good exercise.
(Running is the subject of the sentence.)
3 -- as adjectives
The developing storm grounded our plane.
(Developing is an adjective modifying storm.)
Because we are all intuitively sensitive to the golden rule of modifiers, we can all understand why this is confusing:
The storm grounded our plane, developing.
Right? We can all see that? If the adjective doesn't line up next to the noun it modifies, we have to stop and do the doggie head tilt while we try to parse that sentence. The modifier is misplaced -- literally, not in the place it should be. If there were no word in the sentence which could be modified by the participle, then it would be dangling. That's the difference between a dangling modifier and a misplaced modifier -- danglers have no companion words anywhere in the sentence. (Example: The storm grounded our plane, distracting. What's distracting? Other than the sentence structure, nothing.)
Here's the thing. Hanging a bunch of qualifiers off that participle doesn't change its essential adjectival nature. And that's where we see problems, such as:
The storm grounded our plane, developing without warning.
That sentence is still structurally flawed, even if we have to do less work to parse it while reading it. It's not the plane that develops without warning. Developing without warning is an adjectival phrase which modifies storm, just as developing alone modified storm.
Developing without warning, the storm grounded our plane.
Ah. That's better.
The Legit Exception
There is an important exception -- actually, it's not so much an exception as it is a parallel rule that allows a different outcome in certain circumstances. Are you all familiar with the concept of a cumulative modifier? This is a modifier which qualifies an entire clause rather than a single word in the clause.
She brushed her fingers down his jacket, smoothing it flat, caressing the hint of dust away.
Here we have a main clause followed by two cumulative present participial phrases. How do you know they're cumulative rather than adjectival? This can get a little tricky, but the good news is that it gets easier with practice. Start by isolating the present participle -- smoothing and caressing are the present participles in our sample sentence -- and try to link them back to a noun in the main clause.
Our nouns in this sentence are she, fingers, and jacket. Neither participle can be said to modify any of these nouns specifically. Instead the participial phrases modify the main clause in its entirety. Try this test to check: isolate the participle and move it in front of each noun in turn. Does it make sense?
You might be able to make some arguments here, and there may be other problems with that sample sentence, but these phrases probably pass the placement test.