Angst? What Angst?: Reika considering all she's been through. Her father was murdered in a botched kidnapping, the man she thought was her father was actually the kidnapper/murderer (though it's clear he genuinely loved Reika as his own) who then murdered a man to protect his secret and was then murdered in turn by her long-lost brother who then sacrificed himself to save her with Reika reflexively yelling out "ONIICHAN!" just as he was buried by an avalanche, and she was also kidnapped by her envious, bitter manager in a later case. How this girl hasn't had a nervous breakdown is a feat unto itself.
Critical Research Failure: In "The Santa Slayings," Kindaichi says that the story about Perseus and Medusa tells of how Perseus make Medusa look into his shield, which was shiny enough to be useable as a mirror, in order to make her look at her own face and thus get turned to stone. You don't need to be a scholar to know that this is as wrong as it possibly could be. The myth actually tells of how Perseus looked at the reflection of Medusa in his shield in order to be able to see her without being literally petrified by fear. That was the entire point of the shield, and Kindaichi's version is as wrong as claiming that Superman is strengthened by kryptonite.
Idiot Plot: Smoke and Mirrors featured a murder case that would have been solved incredibly quickly in real life, due to the extreme stupidity of the murderer's way of handling it. To elaborate: The murderer killed a student and hid her body in a wall. Then, he started spreading a ghost story about a student that got murdered in the room where the wall was, so that the students would avoid it. Thing is, if a story about a murdered student starts spreading at the same time as a student goes missing, obviously people will start wondering and subsequently see a connection!
This is also acknowledge in the story itself, when Kindaichi notes that had the culprit simply reported the bodies, he would have gotten a light sentence and been able to live the rest of his life without guilt. Instead, he ended up killing two other students and attempting to murder Miyuki just to cover everything up, and ensured he'd be in prison for life.
Apparently the writer believes in a claim that rumor can't be tracked when and who spread it since similar things happened in "Legend of Amakusa Treasure". To elaborate, the killer spread a rumor about "White-haired Ghost" in less than 3 months before Amakusa Trasure Hunting was conducted. The thing is, even the tour guide assumed that it was an old story passed among children in the village!
Nightmare Fuel: Most cases with a supposedly "supernatural" culprit count. There are many of them. The live action "The Seven Mysteries of the School" ("Smoke and Mirrors" in the U.S. manga translation) case had a scene involving a science lab at night with a jar containing a human head that suddenly... opened its eyes.
Values Dissonance: One case involved a tragedy behind a secret marijuana farm. The portrayal of the MacGuffin in question might seem very excessive in American viewer's eyes but in Japan, marijuana is portrayed as the worst thing ever.