According to producer Steven A. Jones, the original filmed ending has Milo beating Mad Dog in their fight. But test audiences could not accept seeing Robert De Niro getting beaten up by Bill Murray. Universal insisted that the fight scene be reshot and the film was delayed for a year. De Niro and Murray had taken the roles specifically because they were different than the type of roles audiences expected of them. The test audiences also felt Glory was an unsympathetic character so further reshoots were done to portray her as a victim of Milo's control.
In the initial scene when the driver is shot in the head, in order for his blood to have splattered on the window in the manner that it did, the bullet would have had to pass through his head and then through the window.
In the scene at the police station where Wayne is typing up a report while he talks to Frank, he uses white-out to correct a mistake. But since he's using a multi-part form, the typo would only be fixed on the top copy.
In the scene where Wayne is investigating the domestic dispute across the hall, the cop is wearing no top or pants, yet he pulls a badge from his person.