In/spectre is a mystery anime with elements of romance, comedy, yokai, and a bit of horror. Most episodes have the pattern of Iwanagi trying to solve a mystery or explain a mystery. I'll rate the mysteries in my story category.
When I rate an anime, I take five categories into consideration: sound/music, visuals, characters, story, and ending.
The sound effects and background music of this show are good, nothing more or less. The opening is great, and the ending is decent.
The visuals of this anime aren't particularly great, but they aren't bad. I didn't find anything lacking.
Spoiler, click to view
The initial kappa scene where they depict it as a frightening monster has really nice lighting and mood.
There are four prominent characters in the anime. We view the story mostly with a third-person limited perspective from Iwanagi, but we take the same perspective from Saki temporarily. The characters in order of importance are Iwanagi, Kuro, Saki, and Rikka.
Iwanagi has an interesting personality. She's very intelligent and surprisingly agile.
Spoiler, click to view
She moves well in her brief encounter with Steel Lady Nanase despite her leg coming undone. What's ironic about her intelligence is the fact that she seems to be better at applying her knowledge than having it as seen when she repeatedly demands Saki of information. Wisdom is what you know, and Intelligence is how you use what you know. She's a goddess of wisdom, yet she is better at using what she knows rather than knowing what she needs to know. When Iwanagi first demonstrated her playful attitude with romance, I was surprised. "Don't judge a book by its cover" is extremely valid when talking about anime. I expected a cool, calm type. That doesn't mean that this attitude is bad. I like this aspect of her.
Spoiler, click to view
What I don't like, though, is her backstory. I don't understand why she'd be very willing to work as a mediator of yokai and humans when she lost a leg and an eye from dealing with them, but it doesn't bother me too much.
Kuro is an odd character, but I can't explain why without spoiling the anime.
Spoiler, click to view
He has no real motivations, barring his obsession with Rikka which we learn later, and he is essentially a normal guy with a messed up backstory. His origins make pain and fear basically annulled, and this pushes Saki away from him. He's also immortal yet not immortal and can make a possible future reality to some extent. The "romance" between him and Iwanagi seems forced, literally and figuratively.
Spoiler, click to view
The reason for this is because of his lack of motivation. I can see how the two fit together after watching the combo of Iwanagi making possible futures and Kuro solidifying them, but Kuro seems totally uninterested in her. This would make the romance scenes hard to watch if they were taken seriously. The last scene where he compliments her seems like a way of saying that he doesn't have any other options than her, but Iwanagi doesn't seem to see that.
Saki is pretty average. She isn't special, but she isn't a bad character. She's a static, round character like all of the others in this anime.
Spoiler, click to view
Saki's main conflict is her fear of the illogical which stems from her experience with Kuro. Because of this experience, I don't find it hard to watch her become afraid when even just a tiny ghost shows up.
Rikka is a bad character.
Spoiler, click to view
Kuro loves Rikka because of…reasons. She creates a monster of imagination because she wants to become a normal human. Why? Assuming Kuro and Rikka are the same, the anime doesn't say whether Rikka is not capable of dying from old age, it doesn't make sense why Rikka would go to these lengths. Ignoring the possibility that she's just evil, there isn't a reason for her to go to such lengths so she can die from a reason other than old age. She's frail, but we don't have any evidence that says her powers cause her to be that way. Kuro isn't frail. You could say that she wasn't as compatible with the mermaid and kudan as Kuro, but that frailty could be the result of her numerous suicides and not just the initial consumption. We don't have enough information, and that brings us to the conclusion that Rikka shouldn't have been brought up this early. In my opinion, Rikka is a totally meaningless character that isn't needed for an anime like this. Solving mysteries doesn't require a string-pulling antagonist to be in the picture. The only suitable reason for Rikka's existence is to develop a conflict within Kuro that makes him interesting, but because Rikka is such a stupid character, it makes Kuro uninteresting.
Our fourth category is story. We are quickly introduced to the mystery aspect of this anime in the second episode. The mystery in this episode is solved quickly by Iwanagi, but I didn't particularly like the mystery. The most appealing part of a mystery is its ability to be solved before you're told the answer. This mystery doesn't allow you to do so.
Spoiler, click to view
The insertion of pregnancy into the solution is so far out there and not able to be guessed from the evidence provided that it ruins most people's chance at coming to a concrete solution before it's told to them. The second mystery in this story was better, but it ran on too long.
Spoiler, click to view
The four-solution strategy she used to dissuade people from believing in the existence of Steel Lady Nanase wouldn't have worked without Kuro. The anime admits this, but it doesn't detract from the fact that any half-decent strategy could work if Kuro could pull his strings correctly. Rikka pulls several strings as well to help her, but Iwanagi's wits gave Kuro better opportunities. This string-grabbing underscores Iwanagi's intelligence, and I don't particularly like it. In addition to this, the mystery just took way too long. Explaining things is fine, but the constant barrage of explanations can be tiring. Leaving people who don't understand in the dark with a few lights to reach out for is a better idea.
The final category is ending, and the ending to this season wasn't bad. It wrapped up everything pretty well. Despite my critiques, this anime was enjoyable. I don't particularly want a season two, but I don't feel like I wasted my time.