I know Star Trek has done this before but this episode really knocked the concept out of the park.
My favourite part was how it was an episode that seems clearly built around the idea that its audience has already seen this kind of thing before and needs something different to get interested in it. It could've very easily become "Star Trek Discovery 1x07: Cause and Effect Redux," and it was absolutely not that.
Things I loved: it's an anomaly-of-the-week episode, but not! The "anomaly" in question here turns out to sorta-kinda be background dressing for some lovely character building moments. The Ash/Burnham stuff is kinda cute but I could take it or leave it at this point; Burnham and Stamets, on the other hand, was lovely. That's a quietly heartbreaking secret for Burnham to tell Stamets, and the talk he gives Burnham later about how relationships work was a nice touch. It's definitely one of my favourite moments of the series so far. (Also a nice touch: of course they dance in the hallway, because EVERYTHING happens in the hallway; did you notice the two joggers near the beginning of the episode? ha!) And always in the background is the sense that Stamets is Not Right and that this nice Stamets we're getting to know is a hint of potentially bad things in the future.
I never watched very much of TOS and so don't know Mudd. This Mudd was great, though, and he plays better as a direct antagonist on Discovery than as a wildcard in a Klingon prison ship. Plenty of totally understandable anger in him, but a sense of theatrics as well; Mudd's "fifty ways to kill your Lorca" was a surprising bit of levity. He's the kind of antagonist who somehow can get away with twirling his moustache. It sounds like maybe he's going away for good now, which is probably the right move, but I wouldn't mind him showing up again a season or two from now.
The time loop stuff I thought was decently well done. They clearly fast-forward through a lot of the exposition needed to set things up, which is fine but does lead to what feels like sloppiness. How come Mudd's time crystal wristwatch works even when he's dead? (Was he disintegrated? Isn't that a problem?) Does Mudd stay on the ship after the first time loop, when he arrives via space whale (as opposed to having to arrive every time via space whale)? If so, how come he doesn't stay in the same place every loop? How come Stamets seemingly only has to explain things once to people, and then they just kind of already know afterwards? Does Stamets have to explain everything to everyone every loop, and doesn't this eat up precious time? How does Lorca and the rest of the crew act so quickly to prep for the "final loop" when this is probably the first they've heard of it and they only have half an hour? The answer to most of this is that it doesn't matter and would slow down the plot too much, which I suppose is fine and those instincts don't feel wrong. And yet I find myself thinking that I wouldn't mind a little bit of unpacking. Maybe that's the price you pay for everything else.
There's not a lot I don't like about the episode. To get it out of the way: I don't think we need Burnham's personal log at the end. Also, Tilly gets called in again to do a bunch of stuff, which leads to maybe the only real complaint about the episode (and the show to date). So there's a party on Discovery, right? And Ash Tyler gives a speech about how the war's going and we all gotta stick together and we're the best crew and blah blah blah. When did Ash Tyler become so important again? Last episode he just became chief of security. Now the crew is a big happy family that loves Ash, and we've seen none of it. Who are all these people besides Tilly and Tyler and pilot lady who keeps showing up in every episode (this time making out with someone, hott) but still hasn't really talked to anyone on the crew yet?
I think the pace of the show has necessarily had to cut some stuff out to maintain pace, and it feels like the thing that got cut is establishing the crew as, well, a CREW. I wonder if maybe I just need to see more of the bridge crew doing bridge crew things or something, because right now it feels like these characters exist as people but don't necessarily exist as much in terms of their jobs. Tilly doesn't help here because she feels like the most important cadet in the world, given how much she does on the show; as a result, I still don't really know WHAT her job is, exactly. Stamets I think is decently established as the engineer, but Engineering as a place on the ship still feels odd. It's really just, like, a room with a glorified shower stall where sparkly things happen sometimes. Culber is a doctor but hasn't had that much of a chance to do doctor stuff yet. Saru, at least, has taken over as captain and given orders and stuff.
All this can come in time, and it's not necessarily a criticism that will be valid given a few more episodes. It might be the aspect of the show that some people feel is missing, though.