] He's sent the King into a towering rage, and you'd think they'd at least be curious as to why. It's "upon the talk of the poisoning" that Claudius loses it, not when they are talking about the fidelity of Gonzago's wife.

Just to reiterate, in The Mousetrap, the king is murdered by his nephew - not his brother. Shakespeare gives a couple of possible "outs" for the court in this one, IMO: Gertrude's guilt and the plot of the play itself. That could cover a lot of bases of the court members who aren't seeing clearly.

] I think they're just unable to hear and see what's been put in front of them fairly clearly.

Perhaps some of them do, but who would stand up, confront the king in front of the whole court, and risk their position and perhaps their life if they weren't believed. Esp. if based on what Hamlet has to say who has not been, as far as the court is concerned, himself lately? Perhaps some of them were even involved in the plot to murder Hamlet the elder. These poor people risk a real lambasting if they confess and are believed. The poor jerks don't know what to think - Gerturde's guilt, the play plot, suspected murder of Hamlet the elder, involved in the Murder? - better to not risk it.

Also, this is a play about Hamlet, not Lord Joe-Schmoe of the Danish Court. Gotta draw the line somewhere. There are already 5 dead people (at least) at the end of this play. Who needs more? ;-)