Factual error: Basic physics - Hancock throws Michel from a dead stop to above cloud level in about eleven seconds. The clouds are bog standard cumulus which form at around 7,000 metres in temperate zones. This means that Michel accelerates to about 700 metres per second instantly, from a dead stop. Obviously he cannot accelerate during his ascent, so his starting speed has to be at least that. (In fact he would have to start his ascent much, much faster than 700 metres per second as he would be constantly decelerating due to gravity and air resistance, but it will do as a start point.) Michel accelerates from 0 to 2,520 kilometres per hour - twice the speed of sound - in zero seconds. He would be accelerating at around 5000 Gs, turning him into a very long streak of fine, pink mist.
Continuity mistake: In the scene when Mary visits Hancock for the first time at his house, she arrives from the air and crashes down on the ground, after a discussion inside they both walk outside together and Mary is shown getting into a car. In the next shot shown from above the house the car has disappeared and they both fly into the air.
Factual error: When the police are cowering behind their bullet riddled cars, the metal on the bullet holes is bent inwards as if the shots had come from the other direction.
Continuity mistake: (Spoiler Alert) the day after Hancock finds out that Mary also has powers, he stabs her with a large fork with two pointy ends. As expected, they do not puncture her skin. The pointy ends bend toward each other, making a triangle shape. But in the next shot, when Mary snatches it from his hand, the tips are no longer in a triangle shape, just bent the wrong way a little. Mary snatches it away by the handle, so we know that she could not have taken it by the points and bent it.
Factual error: End of the movie, Hancock is in New York with the sun setting. Ray and family are in L.A. with the moon out and no Sun. New York would have nightfall before L.A. would, considering it's 3 hours behind New York.
Continuity mistake: At the start of the movie, when Hancock rips the roof off the car and points to the baddie on his right, watch his right hand finger. First, he points to the man on his right and then to his left. In the next shot he is still pointing to the man on the right and then to his left.