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.