When the deer is shot Harley claims a clean shot through the heart. When they zoom in on the deer the bullet hole can plainly be seen on the neck where the trachea would be, no where near the chest cavity.
In the very first scene, the ambulance has a headlight out on the driver's side as the vehicle is driving towards you. When the scene shifts to the ambulance pulling up in front of the hospital, the headlight is out on the passenger's side of the vehicle.
After the deer is shot by the hunter, within seconds of dying the animals legs appear stiff and suspended in mid-air. Rigamortis does not set in this quickly. The deers limbs should have remained limp.