Recently I re-watched some old Columbo episodes, and I’d forgotten the odd way they were written (at least, the 3 episodes I watched). The killer is actually sort of the protagonist: we, the audience, see the crime take place and observe the killer’s efforts to hide what he’s done. Then, we watch Columbo show up and gradually pick it all apart. Each time Columbo and the killer part company, the script mostly sticks with the killer and his ever-more desperate efforts to avoid exposure; Columbo almost seems like a guest star. They’re kind of the opposite of a “whodunnit” – we know who dunnit before Columbo even appears on screen.
Interesting – I remembered the “Flummoxofin” gag and assumed it was a full repeat. @Uncle $crooge is right, there are several differences. This must be an earlier draft.
I think it would have been even funnier if Dill’s “painted face” had spontaneously switched to an expression of abject terror.