Both times - on different days - when Ann and Remy are talking on the phone, it is either sunset or sunrise outside her office, but it's cloudy, say mid-day, outside Remy's office
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 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.
Anne's necklace just after Daddy Mention is killed.
During the final gunfight, the smoke from DeSoto's gunshot disappears between cuts.
Tugboats are powered by diesel engines. Diesel fuel is incapable of exploding. (Actually diesel can explode fine, it's just not as volatile as petroleum . Plenty of diesel trucks in accidents have both caught fire and exploded.)
The ballistics capabilities at the time (and even now in 2022) would not be able to determine that a bullet came from a MAC-10 pistol.
Obvious stunt players when Remy and Anne run from the about to explode boat.