I just did my first playthrough. I have 40+ years of RPG experience, but very little with solo RPGs. Just this, and a couple of small journaling games. So a more experienced player would perhaps have been better able to deal with some of the issues below.
I enjoyed it, at least after I felt like I got the hang of it. Before that I was pretty confused about how to progress the story. A couple of things contributed to that. First, I wasn't sure if or how much I was meant to be progressing towards a known outcome. In my playthrough, I rolled a mission of Conspiracy (Official bribed). Was I supposed to have already figured out whodunnit, and push my character and scenes in that direction? But if I'm doing that, why not just write a short story instead? Or was I meant to have this conspiracy reveal itself to me via random rolls as I played through? That seems more game-like, but it's also really hard to make that work. Like, would I need to create a bunch of NPCs, each with plausible motivations, etc., then randomize at the end who the actual bad guy was? (I ended up closer to the former than the latter).
Also, I think the game defaulting to having you play the captain is sub-optimal. The sweet spot is probably first officer. As a captain, you are likely delegating most things. You're not the person heading the away mission, you aren't personally firing the main phasers or manning the helm, etc. So your own personal stats, which you spent all that time generating, become less useful. You're just using the ship/department stats over and over. Or else you have to contrive reasons why you as captain are doing all these things yourself. As first officer you'd have a lot more ready-made reasons to be down on the planet, mixing it up with the NPCs directly, etc. The book mentions multiple times that you can play as any sort of officer you want, in any kind of fleet, but it defaults to captain (it's the name of the game!), and I think that's a mistake for a solo Star Trek game.
The book could really use an extended example of play. Not just showing you how to roll on the tables and set up the first scene, which the book does fairly well (and which is also covered in blogs and on youtube), but actually walking you through playing an entire act, let's say. There's a lot of advice in the book about how to structure scenes and stories as if you were a screenwriter working on a episode of the show, but this isn't a screenplay, where you control all the dials, and you know where the story is headed at all times. How do you write/play an open-ended story with enough plot structure to keep the action going but without knowing how it will all play out? Or alternatively, how do you make this a game rather than a writing exercise if you know (or at least have an idea about) how things end?
The book could also use literally any discussion at all of hand phasers or disruptors or what have you. I know combat is supposed to be abstract, and I definitely do not want rules about phase pistols vs. TNG dustbuster phasers. But I found myself in a situation where I obviously would have just stunned a bad guy, and found that there was nothing in the combat rules in between Kirk-fu and photon torpedoes.
As I say, once I was able to get into the swing of things, I enjoyed it, and will definitely try another playthrough. I might demote my captain, though!