When the Chief is talking to Jimmy Dawes in his jail cell, Jimmy goes back and forth between sitting on his bunk and leaning back on one elbow whenever they change camera angles.
At ~5:37 when Virgil is first talking to the victim, Mrs. Casey, in the hospital, there are deep purple bruises around her right eye. The next day when she's at the police station to identify the perpetrator in a line-up, (at ~11:42) there's a lesser amount of bruising shown on the left side of her face and no bruising at all on the right side. The deep purple bruise under her right eye has disappeared and comes back at ~21:25.
When Althea goes into the cafe, Gillespie is sitting with his back to the front door, something a trained police officer wouldn't do. Police are taught to sit facing the entrance, preferably from the rear.