Now and then he'd press his ear against the door and listen to his parents argue/arguing in the hallway.
Do the two options have the same meaning? Or they mean slightly different things?
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Listen to them arguing.
Here, you denote continuity of action, through the usage of the participial phrase "arguing", which is a present participle (and not gerund). So you just highlight the fact that some two people are arguing and you want the addressed person to listen to the same. Nothing special.
Listen to them argue.
Here, you are exemplifying their act of arguing. You choose to use the verb "argue" in the present indefinite tense, which says nothing about whether the argument is going on or not in the present. But there is subtle indication in this sentence that you want the listener to listen to the argument no matter in which indefinite period it occurs. It's as if you are exemplifying the act of argument between two people. Like:
Listen to his parents argue. No cursing, no accusations, no guilt tripping. They talk and solve actual problems like adults.
So I think there's a subtle difference in meaning.