The investigation is pretty clearly written at a high level. I like the detailed character descriptions, I think that's important for an investigation game. I do think there are a few areas that could be shored up:
One small issue is that the easiest hook for the players is sort of implied and left up to the GM. The cover page alludes to the fact that the victim's family is aware something happened and may have reached out to the players and sent them to investigate. However, that's not really stated anywhere. I think that could be fixed by adding one sentence on the introduction page.
The biggest thing I can think of is providing more evidence/clues, even if it's in the form of a list of clues for the GM to reference. I'm reading Act 1 which states that the players find Clara McGee. I assumed that implies they're sent to her by the victim's family. However, it's written as if she's the one giving them the lead in the first place. That might be something that can be cleaned up with a rewrite of the adventure hook. I'd also try to introduce Director Sterling before the investigation begins somehow, rather than pulling him in if the party runs out of steam without any preamble. Maybe Clara tells them to watch out for him, that he's been poking around and could be useful in a pinch, but he's only interested in the money.
Either way, Clara sends them to the Manor where they find signs of struggle and some workers tell them to go to the clinic to see another victim. I'd recommend inserting something here telling the GM that this is a good place for the players to find subtle clues pointing them to The Apothecary and the Observatory. Maybe they find a prescription for the cure referenced on the intro page that would send them to the Apothecary. Maybe they can see the observatory really clearly from the window of the Manor. Maybe the manor staff tell them that the sheriff had no interest in a real investigation, which sends them down that rabbit hole. These might be unnecessary if the party is able to wake Genevieve and get the information directly, but if they're not, then they just sort of have to wander around (the seemingly big city with spread out locations of interest) until they find something or the GM has to pull The Director Sterling ripcord, when it would have been more satisfying to have already buried it in there earlier in the story.
If the players somehow manage to lose the thread of the investigation, then you have Director Sterling, set up at the beginning of the adventure who can come in and connect the dots for the party, showing them the connections they missed and the things they failed to investigate. That can then usher them onto the final conflict in Act 4.
Lastly, I think the map might be doing the rest of the module a little bit of a disservice. The city appears to be much bigger than the rest of the document implies. I think that if a GM were to take that at face value, it could lead to the different locations feeling too disconnected. I think crunching everything down into a smaller package would help with making it feel tied together. And also make it feel much less intimidating if the party does end up in a situation where they're wandering around looking for clues with no real direction.
I think there's the potential to either combine some locations or to bake in a few red herrings in locations that can lead the players to dead ends. I don't see any reference to The Saloon in the text of the adventure itself. I'm assuming that it's there as a stand in for where the players are staying. I think that that would be a great place to seed some red herrings in the form of rumors circulating around the murder. The Observatory is noted as where they can learn about the comet, but it doesn't appear to have any relation to the cult. I'd recommend that that location also include some revelations about the cult baked in.
Overall, I think it has a lot of character, but could benefit a lot from more focus on the investigation itself.