During the grave side service is raining heavily yet the sky is blue and there are sharp shadows from umbrellas.
When Max shoots his front door from inside his apartment, there are three bullet holes. As Max and The Chief leave the apartment, there are no bullet holes on the door's reverse.
Adrian Listenger is on a second floor balcony overlooking Max and Chief. Max and Chief shoot him many times. Seconds later, mortally wounded, Adrian Listenger emerges from the front door of the building (located on the first floor, of course), walks a few steps and drops dead. He could not have gotten from the second to first floor that quickly in his near-death condition.
As Max and the Chief leave the Twin Oaks restaurant and disagree about who will go first, Max says, "But your car is parked in front of mine, I have to pull mine out". However, the Chief had arrived after Max and parked directly behind Max's car, thus Max had room to pull out.