A cheerful man named Professor Berlinghoff Rasmussen (Matt Frewer, of Max Headroom fame at the time) appears before the Enterprise in a small shuttlecraft and claims he is a historian from the 26th century ... and that he has traveled back to the 24th century to witness history — specifically today — as it unfolds. Meanwhile, the Enterprise rushes to help a planet in terrible danger from atmospheric dust caused from an asteroid impact. A nuclear winter may be imminent. They must figure out a way to save the planet and its population of millions from the environmental catastrophe.
"A Matter of Time" is a story that stares the notion of a time paradox in the face and hope it blinks. The crew wants to know why Rasmussen has picked this day, of all days, to learn about the Enterprise and the 24th century. Rasmussen cites what is essentially the Temporal Prime Directive in explaining why he cannot drop any hints about what will happen or how the crew is involved in it. Could it possibly be tied to the planet facing the imminent catastrophe and the decisions Picard will have to make that could save or doom millions?
There's a scene midway through this episode between Picard and Rasmussen that is clearly meant as the centerpiece of the show, where Picard asks Rasmussen for help, and they argue over the ethics of Picard gaining access to information from the future if it means maybe saving millions of lives. It's one of those earnest Trekkian dialogue pieces that seems to be really striving to get somewhere thoughtful and interesting ... but it doesn't quite find its way to a point. Through all of Picard's pontificating and Rasmussen's evasions, they're ultimately just talking in circles and nothing is gained. Eventually I was waiting for crazed Doc Brown to show up, shouting, "It's your kids, Marty! Something's gotta be done about your kids!"
And if there's a bigger problem with "A Matter of Time," it's Rasmussen himself. It becomes difficult to stand the guy after a while, particularly once we know he's up to something fishy (we see him stealing components from various places on the ship). He's the sort of guy who finds an obnoxious and condescending way to make an allegedly wondrous 24th century historic moment all about ... himself. He claims to be a history buff, but he seems more like an overbearing kid trying to shoplift in a candy store while telling you how awesome you are. I tend to think a real observer from the 26th century wouldn't divulge the truth of his origins to those he's observing, and you'd think Picard would be more skeptical given that logical loophole. How does the saying go? You can't study something without inadvertently affecting its outcome. That goes double for time travel. Hell, just talking to Picard could cause the entire future to be erased (like it was/is/will be in Star Trek XI).
I guess we're supposed to find Rasmussen annoying, so we can enjoy the twist and his undoing; it turns out he's actually a con man from the 22nd century, who stole the time shuttle from a guy who was really from the 26th century and came to the 24th century to steal gadgets he could travel back in time to "invent." The scene where the crew confronts him over his thefts is kind of fun. (Data, making a matter-of-fact threat: "I suspect your hand will activate the panel that opens the door whether or not you are conscious.") But I must protest: If you cause a guy from the 22nd century to become trapped in the 24th century, haven't you just changed the past? Or was it always that way???