When Molly is talking to the deaf gunman in the hospital, the view through the hospital window shows an area devoid of snow, even through the gun battle was supposed to have taken place during a blizzard with snow accumulations in excess of 18".
The opening scene is shown as if it were being played in reverse, but the nurse in the foreground is obviously walking backwards to simulate a reverse scene.
There is no reason police would be granted an immediate search warrant for a home after a child brings a gun to school. The proper protocol would be to question the parents first and see if the gun was connected to any crimes, which in this case it was not.
Two FBI agents sitting in a car 25 feet from the building Malvo enters do not hear a gunfight happening that's several minutes long, yet hear a body falling out the window instead.