Taking the groceries from her, he put the lettuce away in the fridge, pouring a glass of juice as she went back out into the hall, bringing back the case of beer.
Participles are supposed to show simultaneous or near simultaneous action, and as such, they are NOT appropriate for a sequence of action. He cannot possibly simultaneously take the groceries from her, put the lettuce away, pour himself juice... not even if he has four hands (need the groceries in hand before he can put the lettuce away). And she cannot simultaneously give him the groceries, go back into the hall, and bring back the case of beer.
If the writer had not given into the temptation to use participles, he would have had to actually describe the sequence of events, and perhaps even use time terms like "first" and "then". Just that would have forced more understanding of which actions are truly simultaneous and which are causal or sequential. He might even -- shockaroo-- have done this in TWO sentences. Heck, one of those sentences might have been a declarative sentence starting with the subject (he).
Let's try it.He took the groceries from her and put the lettuce away in the fridge. While he poured a glass of juice, she went back out into the hall and returned with the case of beer.
Now why do so many good writers avoid the absolute building block of English syntax, the declarative SVO (subject-verb-object) sentence? Certainly ALL sentences shouldn't be SVO, but many should be. Never go out of your way to avoid SVO. If you have three like that in a row, sure, look for alternative openings, but try to do that without a participial phrase. Prepositional phrases and dependent clauses are much more graceful and will seldom leave me wheezing with that mingle of laughter and gagging.