Wax Doll Castle Murder Case: File 2 - S1-E8
Character mistake: Hajime's proposed solution is obviously wrong, but not for the reason they mention; the 'killer' could never clean themselves up completely and effortlessly in such a short time from the soot.
Gentleman Thief's Murder: File 3 - S1-E12
Character mistake: Itsuki tells Kindaichi about the painting the strange man was doing, saying it was "My Beloved Daughter." That is incorrect though, since what Itsuki would have been able to gather from the hospital staff was that the man painted lavender fields literally all over the room. The staff would remember that (a whole room of the building was changed!) and not that specific painting - and if they knew about it, news of it would have spread, being one of the most famous paintings in the world.
Opera House Murder Case: File 1 - S1-E21
Character mistake: The brother of the dead actress, Fuyuko Tsukishima, stares intently at her diary. On its cover; "F. Tukishima", missing the S. (00:12:45)
Opera House Murder Case: File 2 - S1-E22
Character mistake: Like the previous episode, Fuyuko Tsukishima's name is transliterated wrongly in "Tukishima" on the cover of the diary.
Ghost Passenger Ship Murder Case: File 2 - S2-E6
Character mistake: During Wakaouji's flashback, if he really picked the picture from his breast pocket the way it is depicted, then the picture he showed to the captain was upside down. Would be kinda hilarious, but I don't think that is what the animators were going for. (00:16:35)
Magical Express Murder Case: File 1 - S2-E10
Character mistake: When the boss of the magical troupe greets the passengers, the clock behind him shows it's 9:40. Noble later complains that he's gone for over an hour, but when he performs the stripping trick on Miyuki, the clock shows it's a couple minutes past 10, so not even half an hour passed. (00:07:40)
Magical Express Murder Case: File 3 - S2-E12
Character mistake: In Akechi's flashback, the board with the flight for Los Angeles has accurate names of airline companies (they seem to have swapped "Virgin" with "Kristen", for some reason) but the flights for Seoul is from "KSREAN" Air, clear misspelling of "Korean." (00:14:15)