When Ann, Remy, and his four family members meet in the PD garage to serve the search warrant, all four of the uniformed officers are wearing their hats as they begin to enter the station. But, when the shot changes to the interior, none of the officers has a hat at all.
When Remy is getting dressed before going to the Storyville Triple Murder scene, he has his shirt, tie and jacket on when he asks if she's sure that he should come back, while standing at the foot of the bed. In the next shot, he is in the doorway with his shirt on but completely unbuttoned, and his jacket and tie over his arm.
When Anne calls Remy to apologize for leaving his apartment so abruptly that morning (when she first met Remy's brother), it looks as though she's calling at dusk or nightfall. The view out her office window is darkened. Yet, when Remy is shown talking to her from his office at the police station, it's bright and sunny outside. The sun is shining brightly and it looks to be high-noon. Not so on Anne's end, where outside it looks to be dusk, or later.