Plot hole: After Jack's wife disappears for a couple of days, he receives a call from her cell phone from the cab driver who found it. Jack arranges to pick it up from a hotel. After he picks up the phone, its battery dies as he checks it, at 12:13pm. In the next scene with Jack, he's in a bar with the phone plugged into a charger; when it comes on, he checks it - the battery shows 3%, but the time is 9:13pm. He apparently wasted 9 hours when he's in pursuit of his wife's mysterious disappearance before plugging in the phone. A scene later, the time is now just a minute later at 9:14pm but the battery is now charged to 79%. (00:37:25 - 00:40:45)
Inspector Kenmochi the Murderer File 2 - S1-E20
Plot hole: The brief intermission when Busujima meets the 'killer', or at least the person wearing the hat, does not make sense plot-wise and is merely a dishonest way to trick the audience. It's not even something Busujima tells someone, so it can't be characterized as a 'unreliable narrator' device. (00:18:30)