Other mistake: As Red goes to shoot Hancock, there's no bullets or shells in the cylinder.
Visible crew/equipment: White squared screens used for lighting are reflected on Hancock's glasses most of the time throughout the movie.
Factual error: When Hancock saves Ray's life by stopping the train, stopping the train instantly like that would have caused it to violently derail, likely killing everyone on the train, and causing massive damage to the entire neighborhood.
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.
Suggested correction: It is nighttime in both locations. In New York, there is a dim glow in the sky due to light pollution. This the same reason it is almost impossible to see any stars in the night sky in New York City. Also, a full moon that far above the horizon is only possible at nighttime, and we see Hancock look up at the moon, so again it is nighttime in NYC.
Factual error: When Hancock is upset that his bottle is smashed, he puts his feet through the bottom of the vehicle, stopping it. In the long shot, the SUV stops slow enough that the occupants would have been pushed forward, not slammed into the windshield.
Continuity mistake: During the battle between John and Mary, a huge storm brews up above and around them. Shots of Ray having a meeting show this storm outside the window. But just before the office is torn open, a momentary close-up of Ray in the office shows a normal, late-day sunny sky, then the wall is ripped open and the gray/blue storm is there again.
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.
Revealing mistake: When Mary and Hancock are fighting throughout the city, they hit buildings, pavement, etc., doing massive damage, but their clothes are almost completely unaffected and are barely dirty.
Visible crew/equipment: As the camera looks at the female cop pinned down, the crane used for the high fly stunts is reflected in the car's finish.
Continuity mistake: As Ray gets done with the call with Hancock, his hand starts to drop. In the wide shot his hand is back up by his ear.
Visible crew/equipment: As the guys in the SUV look around, the studio lighting is reflected in their shades.
Visible crew/equipment: After waking up on the bench, Hancock puts on his shades. As he looks around, the studio light reflector is seen in his shades.
Continuity mistake: At dinner, after Hancock tells his story, Mary is crying, with tears on her right cheek. A few seconds later, a close up on her face shows that her cheek is perfectly dry, and made up.
Continuity mistake: When Hancock is coming up on the SUV in the beginning, he has a bottle of whiskey in his left hand. When he lands and goes to rip off the roof of the SUV, you see his left hand empty (except for a handful of roof). After opening the vehicle, you see him fly backwards, and you see that he has the bottle in hand again.
Suggested correction: If you watch it again, you see after he rips the roof off and goes flying backward, the bottle actually flies back with him, and he actually grabs it. So he tucked it away or set it somewhere while off-screen to rip the roof off.
Continuity mistake: At the very end of the movie, just before the credits, there is a scene where a criminal (Mike Epps, uncredited) is running from the New York Police. In the first shot of him, he has a gun in his hand. Then he runs out in the street and stops as he is surrounded by the police. At that point, he does not have a gun. Then, as he grabs a hostage, he suddenly has a gun again right before Hancock lands to help apprehend him.
Continuity mistake: When Ray is running to City Hall he interrupts an animal rights rally, then gets his right foot stuck inside a cello, and when he finally gets it out you can see that his shoe came off, but as he's escaping up the waterfalls his shoe is back on.