I read a story a long time ago, I think in a short story collection. The main idea was that a TV had been invented that could be set to any place and time in the past, and you could see what happened there and then.
Anybody know what it was?
Sounds like The Dead Past by Asimov, where there is a very rare device like a television called the Chronoscope that can look at events that in the very distant history. The story goes on to reveal that the chronoscope can in fact:
Only view up to a little over one hundred years in the past, but importantly it can
view up to the immediate past, essentially the 'living present', making it a device
that could destroy privacy for anyone on the planet.
As a result, in an attempt to keep this fact secret, and to prevent smaller and cheaper chronoscope's being invented, scientific freedom is rigidly controlled by the government, research outside your field being banned and with the techniques required to develop a Chronoscope being mysteriously unfunded.
You can see an adaptation of the story on YouTube.
There's also Damon Knight's "I See You" about an inventor who, as anonymously as possible, creates and distributes a machine which allows people to view anything that happened at any time, completely eliminating crime and also privacy.
E for Effort by T. L. Sherred comes to mind.
It's not presented so much as a television, but Orson Scott Card's "Pastwatch: The redemption of Christopher Columbus" (one of Card's better books even if it is preachy and I completely disagree with its premise) has a device that lets the past be viewed.
This is unlikely to be the story you were thinking of as it is a full novel, but The Light of Other Days by Stephen Baxter, based on a synopsis by Arthur C Clarke, deals with the same premise. I remember reading it and thinking it was overly similar to Asimov's The Dead Past, which was suggested above.