This is a series of ups and downs. It's hard to give one definitive opinion, for reasons I'll explain below.
First, the story. It's not a linear path to the finish. After using the first arc to introduce the primary cast, each arc just kind of happens when it happens. Rather than every action in the story informing the next, we have loosely connected or non-connected arcs. Obviously linear isn't a simile for good. Plenty of stories can be episodic and great. But that requires each episode to be great.
Put simply, some arcs are great, and some are meh. No arc went below 'meh', and some arcs were amazing.
As for the plot specifics, it's in the title. Each arc focuses around our key detective, Eiji, and his power of "Psychometrer". Anything he touches and focuses on, he's able to get glimpses of events surrounding this object. After a detective finds this out, she employs his help on cases so as to have a greater edge on prospective villains.
While the story is primarily mystery, some arcs take an effort to add drama beyond the mystery aspect. Even if the villain is known, they can still do plenty to affect the plot. Arcs tend to be a nice blend of action and mystery, thus providing variety for the reader while simultaneously engaging the reader.
It's a cliche statement that a hero is only as great as the villain, but I think it applies to story quality as well. Most of the arcs with a more generic villain leave me less invested in what's going on even before I know the villain's identity.
While the stories are certainly dramatic, it has some questionable moment. I am referring both to plot contrivances and its handling of most female characters. Nine times out of ten, the victims in cases are females from a perverted killer. I wouldn't mind this as much if some of those females weren't given moments of spotlight only to soon be killed off. It killed my narrative appetite a bit, seeing a character given depth only to use her death to fuel someone else's story. It felt cheap. There's also a couple plot contrivances towards a few of the mysteries, but they aren't super distracting. Not the ones based on real world physics, that is.
By that I mean, the Psychometrer power itself. Its ability is somewhat vague, leaving it as a product of a soft magic system. This hurts the story as any supernatural ability used to solve mysteries should be hard magic, so that specific rules must be followed that the audience can know ahead of time. As a result, Eiji can see either an hour back on the object he touched, sometimes in blurry images. But it can be from the perspective of a human he's touching, but then he sees the person? Wait, now it's a number of years back? He can sense the world around him? Suddenly he's influenced by those he has used his psychometrer ability on? It's exhausting, but how much use leads to becoming comatose?
Psychometrer Eiji takes place mostly in the real world, and those mechanics are arguably more important than a psychic power meant to be a mystery even to Eiji himself. But I think it's a nit worth picking.
The story has some filler too. I don't see filler as an abject evil, I think taking a breather from heavy events can help flesh out characters. And for the main cast, I find that it does. Seeing them hang out and do goofy stuff makes them feel a bit more human. Though there are some filler chapters featuring this ugly looking frog who either has no agency or gets involved in weird pervy shit. I ended up skipping the chapters he was involved in, and I'm glad they were filler. He's had me give the story a 7 rather than an 8. Luckily he can be ignored when reading.
Next, the cast. I can't give a straightforward number here because some of the characters are really good. But others suuuuuuuuuucked.
A good one is the protagonist, Eiji. He's hot-headed and emotional, yet good in a fight and able to process things in a pinch. We get a chance to explore how his ability gave him a greater awareness of the world around him than he was ready for, leaving him unsociable for much of his life. All of these factors make Eiji a well-rounded character, and also make his stupid actions more plausible than if an adult were acting as he did.
Some of the side cast is great, too. Toru leads his own small gang, yet has a complicated family life and does small jobs to maintain his personal surroundings. Yuusuke doesn't have much on the fighting spectrum, but he's smart and provides a sense of comraderie with Eiji that Eiji might have developed with Toru over the manga's duration, and certainly no one else.
And now for the bad. Shima makes for a good transition because she was a good character. A single female in her 20s trying to make a name for herself. The first few arcs feature her struggling to get her voice heard even as the police act on misleading information. She would show incompetence when faced with a certain character, and at first I liked that, foils and all helping her understand her own shortcomings. But she didn't learn. As the story went on, she got worse as a cop, and served as more of a vehicle than a character struggling to overcome her shortcomings. Sometimes she outright depends on Eiji's psychometry, not even trying another method and seeming rather flippant about exhausting volunteer help. I don't mind a bickering dynamic, hell Toru and Eiji do more damage to each other than the villains and I consider them best friend goals, but an adult badgering a high schooler for volunteer services should be mindful of how far she pushes him.
Then we have Emi, Eiji's brother. She's a bro-con (ugh, but luckily it's minor enough to be ignored), and whenever she has an important role in the story, it's as a victim. I don't need her busting skulls. Hell, if she stayed ignorant of Eiji's suspenseful life, I'd be okay with her not doing a damn thing. But she's aware of Eiji's circumstances, and despite the bro-conness, she doesn't do anything to help Eiji understand his powers, or even offer Eiji anything back as she makes all sorts of minor demands for him.
Apart from them...uh...we get a few cool minor characters during the story. Shima's boss is treated as a gag even when he's just asking Shima to do her job...alright, enough stalling.
Lastly, the villains. This is a tricky talking point because of the mystery genre, and to mention name or describe qualities would count as spoilers. I consider most of the villains rather meh. This is a bit more forgiveable in a mystery story, because the goal is finding the killer.
Luckily, there are two fantastic villains who do an amazing job in their respective arcs, and get significance beyond them. I may do a spoiler review so I can gush about them, but I want to get better at writing reviews before I do that. All I'll say is, I'd rather one of these villains have been controlling Monokuma from Danganronpa. Not the other, their personality isn't so blanketly evil that they could.
Nothing too much to say about the art. It has a great 90's aesthetic, making the characters look like humans. A lot of detail goes into the backgrounds, and the psychometrer visuals do a great job both revealing and hiding information.
There's a certain bit of simplicity added in as the story goes on. It's most noted in Shima, who went from smoking hot to a 40 year old using plastic surgery to look young. I get that she's meant to feel 'old' compared to the high school cast, but use less plastic, please.
I also felt like there was little spectrum between hot and ugly in the cast. You either have a striking design, or over the top or outright ugly. There are multiple ways to draw faces.
But I'm not an artist, so take those last two criticisms with a grain of low-quality solvent.
A number of arcs are great. Some are meh. Also, there's filler. As a package, it's a 7, but some story aspects are better than the others, and since I skipped around some of the filler, I can't say the bad in one arc necessarily affects others.