Opera House Murder Case: File 3 - S1-E23
Plot hole: For Kiryu's murder, the killer's trick consisted in the fact that he wore her shoes after hanging her with a cable while she looked down from the window. First of all, it would have never worked as shown and the cable would have clutched her shoulders and arms rather than wrapping around the perfect spot on her neck to trick people to think she was hanged. Second, she was in her room and most likely not wearing shoes, thirdly; he'd still would have left a mark putting her shoes on unless he did it in midair, but still unless she had unusually big feet they would have never fitted him, and he couldn't leave the perfect prints that resulted.
Opera House Murder Case: File 3 - S1-E23
Plot hole: In the first episode, Hidaka screamed twice, but nobody heard the first scream, and everyone instantly came when they heard the second, but couldn't hear the sound of the crashing chandelier. She herself did not hear the alarm bell, but that is explained; trouble is, the fact that a curtain could make the stage totally soundproof is just impossible. A thick stage curtain can dampen the noise but not nullify it.
Hida Mechanical Mansion Murder Case: File 3 - S1-E20
Plot hole: The plot is based on the fact that a certain character was disguised as the presumed first victim. At the same time, the two characters have a different body type (otherwise the gap in the window would be obviously too small), so the turn of events does not make sense. Moreover, supposedly the victim suffered serious burns in a fire, which would be absent in the corpse.
Hiren Lake Legend Murder Case: File 3 - S1-E6
Plot hole: As it often happens in this sort of murder mystery, there's a switching act at one point, and one of the 'disfigured bodies' is not who it is presumed to be. Good, but the problem is that the presumed victim and the person who really died have radically different skin tones, and it'd be practically impossible for anyone who knows them to mix them up - even moreso for the genius detective Hajime Kindaichi.
Academy's Seven Mysteries Murder Case: File 3 - S1-E3
Plot hole: A corpse has been buried inside the walls of the building for 10 years. It's covered by just a poster, and a poster from a current high schooler. If we assume the first victim was the one who put the poster there, then it means that it was just randomly uncovered by the earthquake from episode 1, which would make the chain of coincidences nothing short than miraculous. She basically one day said "I heard there was a murder here where we all hang out all the time" and the ground by its own accord opened to reveal a skeleton without her doing anything.
Opera House Murder Case: File 3 - S1-E23
Plot hole: So the culprit checked in at a hotel without any document or... face, left the room right away using an inflatable boat contained in a medium size suitcase (which he left in the room) and with that reached the coast - because the hotel is on an island so remote that it took a relatively long trip by ship for the others to reach it. It's a plan all kinds of ludicrous and impossible - that's also without considering the fact that the hotel was booked by the cast of a Phantom of the Opera play and the staff knows the play, and one person hiding their face completely would be a pretty big coincidence they make nothing of.
Opera House Murder Case: File 3 - S1-E23
Plot hole: For the murder to happen, the killer needed to be next to the alarm bell and at the same time up in the stage rafter to cut the support cable, all while making sure the victim stayed exactly on the spot she needed to be for this demented trap to work.
Hida Mechanical Mansion Murder Case: File 3 - S1-E20
Plot hole: Even considering the fact that the corridor was dimly lit (but not in complete darkness), it is impossible to plan the 'switch' the way it happened. For the plan to work, the killer needed to go through a revolving door at the same time as Kindaichi; there was no guarantee which of the two halves of the door he'd make spin, though, and he needed precise timing (against someone running through the door at full speed) and not make a sound with the keys he was carrying. The corridor (and therefore the door) is also so narrow that you wouldn't be able to ever pull it off.
Hida Mechanical Mansion Murder Case: File 1 - S1-E18
Plot hole: At the beginning of the episode, Kindaichi and his friends have an encounter with the mysterious figure that will be murdered later (allegedly). Three episodes later the identity of this mysterious figure is revealed, creating an impossibility when you consider who played that role. (00:03:10)
Wax Doll Castle Murder Case: File 3 - S1-E9
Plot hole: Miyuki is not a detective or has any qualification in the world of crime novel. Her presence (taking up one of the 10 slots of detectives picked from all over the world, she's not an accessory to Kindaichi) is completely unexplained and nobody questions it at all.
Wax Doll Castle Murder Case: File 3 - S1-E9
Plot hole: According to what was established in the first episode of the arc, the statute of limitations for the crime has expired. In this third one though, it is said that they are afraid that the body will be discovered. There's no link between them and the victim (s), so to say that they joined the whole madness because they needed to prevent the castle from being 'moved' is absurd.
Hiren Lake Legend Murder Case: File 3 - S1-E6
Plot hole: Kindaichi's denouement can happen only because the killer misses half a dozen people leaving the cottage covertly; Kindaichi does not have a clue of the killer's observation point, and despite what the detective says, the killer was not just listening, but watching them too with binoculars. Moreover, moving a microphone sensitive enough to capture the sounds of the whole room would produce noises which would have alerted the killer that they were tampering with it.
Hiren Lake Legend Murder Case: File 3 - S1-E6
Plot hole: The plan of the killer relies on a couple of pretty strong coincidences, such as the fact that they wouldn't realise their common link (he knows nothing about what happened on the cruise, so he couldn't know that they all wouldn't realise they have met before) and the fact that the boat is discovered at the perfect time for him to commit murder (on someone who wasn't part of the trip, but is willing to join him).