Aha! Thanks to Oldcat's post about Prototaph, I found Thinking Machine, published by Raintree Publishers, which was in a different book in the series put out by that publisher, which led me to Tomorrow's TV.
The story is A Scientific Fact by Jack C. Haldeman II. The catatonia consists of the person endlessly repeating the last word they'd said, and starts with a radio jockey who'd locked himself in the studio, with people initially thinking it was a prank that he kept repeating "hit" over and over again. I also underestimated the figures for the number of images and why it was so overwhelming:
"Exactly. You may not know this, Mr. Woods, but television is produced by a rolling scan of 525 lines thirty times a second. Although the alert mind connects all these separate things into continuous action, somewhere, deep in the brain, all these separate pictures are counted, stacked up and filed away. Soon we are all filled up like the box! And us... aha!"
For the other stories, it was indeed PrototaphPrototaph for the one about the insurance policy, Wapshot's Demon for the Maxwell's Demon bit. It actually gives answers to "yes or no" questions. Man of Distinction was in the same anthology as Wapshot's Demon, Wild Inventions.
Man, those were some quality books... I'm going to have to look them up again when I get home.