Styjun

When I started reading science fiction in 1987, I read a lot of “best of” collections and believe I found this story in one. To the best of my recollection, the story involves a man who invents a screen to watch history unfold. He watches the jfk assassination and can view all angles and sees a man on the grassy knoll. As he updates his machine, people use it to watch life unfold in real time. A man sees his wife entering a motel with another man and the husband tracks her down to shoot them.

Possibly "I See You" by Damon Knight, which has indeed been collected in a number of "Best Of" anthologies.

The story jumps back and forth, mostly a second person tale of someone who grew up in the age of ubiquitous time viewer use, but it also talks about the origins, in which the inventor of the time viewer does in fact look back on the Kennedy Assassination:

By trial and error, Smith has found the settings for Dallas, November 22, 1963: Dealey Plaza, 12:25 p.m. He sees the Presidential motorcade making the turn onto Elm Street. Kennedy slumps forward, raising his hands to his throat. Smith presses a button to hold the moment in time. He scans behind the motorcade, finds the sixth floor of the Book Depository Building, finds the window. There is no one behind the barricade of cartons; the room is empty. He scans the nearby ·rooms, finds nothing. He tries the floor below. At an open window a man kneels, holding a high-powered rifle. Smith photographs him. He returns to the motorcade, watches as the second shot strikes the President. He freezes time again, scans the surrounding buildings, finds a second marksman on a roof, photographs him. Back to the motorcade.

Eventually the device gets out to public use, and it does contain a scene where a husband spots his wife having an affair... however, he's stopped before shooting her by someone spying on him (at least presumably, the story doesn't elaborate on their fate after the conversation):

In a house in Cleveland, a man watches his brother-in-law in the next room, who is watching his wife getting out of a taxi. She goes into the lobby of an apartment building. The husband watches as she gets into the elevator, rides to the fourth floor. She rings the bell beside the door marked 410. The door opens; a dark-haired man takes her in his arms; they kiss.

The brother-in-law meets him in the hall. "Don't do it, Charlie."

"Get out of my way."

"I'm not going to get out of your way, and I tell you, don't do it. Not now and not later."

"Why the hell shouldn't I?"

"Because if you do I'll kill you. If you want a divorce, OK, get a divorce. But don't lay a hand on her or I'll find you the farthest place you can go."

This isn't the story you are looking for, but there is a novel by Arthur C. Clarke with a very similar premise called The Light Of Other Days.

I would recommend.

It focuses on the fact that this technology creates societal change due to the fact that privacy is destroyed overnight, as anyone can spy one anyone else throughout history.