After the police officer is attacked by the bird and rolls his car down the bank, we see that the car is clearly about to come to rest upright. But subsequently we see the car upside down as it catches fire.
Prior to the Inspector's car accident, the chrome front bumper of his blue Buick LaSaber is heavily dented before the vehicle strikes any object. Immediately after actually hitting a few objects, the dent in the bumper disappears. The damage on the car on the driver's side bumper does correspond with where he later struck construction signs and a motorcycle, but appears and disappears before those collisions happen.
During the ice skating spinning sequence, Katie clearly lets go of the boy in the darker blue shirt twice (or the same footage is used twice). The aerial shot shows her letting go of the boy, and then a quick wide shot of them spinning together still holding onto each other, then the aerial shot again shows her letting go of the boy.
When Durham is being attacked by the falcon, in none of the shots from outside the vehicle is there a falcon anywhere.
When Katie is dragging her paralyzed mother up the stairs, face-up by her feet, her smother suddenly appears kneeling, facing Katie. The mother could not do this as she is paralyzed.
Despite the Atlanta basketball team being referred to as the Rebels, there is signage clearly visible for the Atlanta Hawks, the real team that played at the Omni.
Although Mrs Collins is paralyzed from the waist down, she is able to drive a car as if she was not disabled at all.
This is not a mistake, as they have made hand-controls for paraplegics for decades (began after WW2)
At the skating rink, it's unclear why Jerzy is constantly show walking down a stopped escalator.
Before Durham is attacked by the falcon, he identifies himself on radio as 'Inspector one.'
When Barbara is being pulled along the ground a wheel and part of a small skateboard is visible underneath her.