Is this a grammatical error? What type of clause is this?

All three sentences need to begin with “Whilst” or “While.” Plus, it will be tedious if the author uses the same sentence structure constantly. Generally, one wants to mix sentences of different lengths. Also, short sentences tend to evoke tension or suspense, whilst long sentences tend to make the reader comfortable with what’s occurring (unless the sentences are so long and convoluted that they’re difficult and painful to follow).

Those sentences all begin with a subordinate clause consisting of a participial phrase that modifies the subject of the main clause. Your examples are grammatically correct, so it’s not the accursed dangling participle that’s bothering you. Rather, it’s the author’s false sense of economy: it’s a technique for conveying two pieces of information at once without making separate declarative statements of them. Overused, it calls attention to itself. No construction should be resorted to again and again so that you become aware of the repetition and are distracted from the content.

(No, they do not require “while” or “whilst.” That would also be a correct construction, but a different one, an adverbial phrase rather than a participial phrase. There’s no need to spell out the simultaneity; the use of the present participle takes care of that.)

However, two out of three of those examples do have a problem of sense that an editor should have fixed:

—Unless John is cursing for some reason other than the splash of hot coffee, we see him cursing before he spills the coffee; the cursing is in progress at the time that the spilling occurs. If this is cause and effect, it is out of sequence.

—Sarah’s fumbling and opening can’t reasonably occur simultaneously. Presumably she fumbles first and then stops fumbling and opens the door. These two events should be sequential and not concurrent. So it’s not reversed, as in the first example, just illogical.

The third example is ok because it’s possible to laugh and joke while gathering.

Reading over what she has written, I could not improve on what @Jeruba said.

Thanks, @Jeruba! That is exactly what bothered me about it. She’s shoehorning pieces of information together that don’t necessarily belong in the same thought. Something like “Sarah fumbled with her keys and opened the door” would be a lot more readable. And the order of events does need to be straightened out.

I cheered a little when I saw you working on an answer for this. Your formidable grammar skills saved the day again. :)

Yes, excellent answer, @Jeruba!

@Jeruba Very perceptive, informed, and informative!

@Jeruba just the fact that you introduced me to a new word, simultaneity, makes me happy that I read your answer. The rest of your answer just makes me want to bow to your superior grammatical intellect! Three cheers to you!

They are gerunds

Thank you, @all, you’re very kind. I have noticed this sort of bad form even in published novels by popular authors—constructions such as this: “Racing after the train, he slid through the door at the last moment.” Those two things do not happen at the same time. I consider that sloppy writing and a warning sign that the author has not taken as much care as I expect in a book I’m going to spend time reading.

@JonnyCeltics, no, they’re not. A gerund is a participle used as a noun. The present participle in each example is being used as an adjective, not a noun. Here’s an example of using each as a gerund:

•  My mother doesn’t approve of cursing. (“Cursing” is a noun, object of the preposition “of.”)
•  Fumbling with the zipper slowed him down. (“Fumbling” is a noun, subject of the verb “slowed.”)
•  I love joking. (“Joking” is a noun, object of the verb “love.”)

@Jeruba, you are a gem. I appreciate that you know these answers and explain them so well.

I agree with @JonnyCeltics the -ing forms in the example sentences are acting as gerunds not as present participles. They are acting as nouns not as adjectives. Although gerunds are said to function as nouns, they do not lose their verbal properties completely: in the phrase Cursing loudly…cursing is a gerund denoting the action of a verb modified by the adverb loudly but acting as a noun in the clause.
These are examples of present participles acting as adjectives (they keep the position of a normal adjective modifying a noun):
He has held an interesting life.
His life has been interesting.
He has made life interesting.

I’ve changed my mind. The –ing form used in the sentences is in fact the Present Participle. The problem I had at first was the notion that the subordinate clauses were functioning as adjectives. I couldn’t see that, therefore, I thought they had to be gerunds in appositive or relative noun clauses or something like that.

I then found a great explanation that I think sheds more light on the use of the Present Participle in the sentences in question and as I initially suspected, it is not acting as an adjective:

To replace a sentence or part of a sentence:

When two actions occur at the same time, and are done by the same person or thing, we can use a present participle to describe one of them:
• They went out into the snow. They laughed as they went. They went laughing out into the snow.
• He whistled to himself. He walked down the road. Whistling to himself, he walked down the road.

When one action follows very quickly after another done by the same person or thing, we can express the first action with a present participle:
• He put on his coat and left the house. Putting on his coat, he left the house.
• She dropped the gun and put her hands in the air. Dropping the gun, she put her hands in the air.

The present participle can be used instead of a phrase starting as, since, because, and it explains the cause or reason for an action:
• Feeling hungry, he went into the kitchen and opened the fridge.
(= because he felt hungry…)
• Being poor, he didn’t spend much on clothes.
• Knowing that his mother was coming, he cleaned the flat.