Young Kidaichi's Murder: File 1 - S2-E1
Revealing mistake: There's a frame of animation obviously missing when the cameraman moves past the rest of the crowd that gathers after the maid's scream. He basically teleports past Miyuki while his hand is still in the same position it had when he had the hand on her shoulder. (00:14:40)
Magical Express Murder Case: File 1 - S2-E10
Revealing mistake: The train has been evacuated and the manager is looking for the troupe leader. There is something wrong in the train behind him though, because the main body of the train is floating over the wheelset. (00:14:00)
Magical Express Murder Case: File 3 - S2-E12
Revealing mistake: Akechi learns about Reiko Chikamiya's death from the newspaper. It's not a very respectful newspaper, since at first glance you can see in the body of the article a big "DUH." A column away, you can also read "he's the best running back in the X-league", which certainly the middle aged woman wasn't. (00:15:40)