I didn't think it was overacting Falk has a way of capturing your attention. He had me watching to see what he was going to do next. The writing I thought gave Falk something to really act on. Also the concept Rod Serling came up with to show the paranoia of Castro was clever.

A few times Falk reverted to his New York accent, I was surprised they left that in but I didn't think it took away from the drama at all.

Not to get too political, but along with the paranoia of Castro, a lot of people see paranoia ABOUT him in the story. But either way, it's entertaining.
Maybe Peter is a little "broad" as a Latin American character, but Antony Carbone is even MORE broad (but in an entertaining way).