When the train comes to a halt, the freight car behind the locomotive is a gondola. When Hancock walks around the locomotive and sees the rest of the train piling up behind it, the gondola is now a boxcar.
During the shootout outside the bank, the bullet holes in the police cruisers are dented in, as if they were fired from the side of the car the officers are hiding on. If the bullets were coming from the other side, the holes should be bent outward.
Hancock leaps into the air in front of Ray's house and after retrieving the ball outside of the prison yard. The (cgi) debris thrown into the air in each place is the same despite the road / ground surfaces being different. One is ashphalt, the other is sandy.
When the people are running away from the tornadoes, suddenly a strange character runs from the left to the right of the screen. The character is twice as tall as everyone else, and looks like a robot or an alien. It may be a street performer, on stilts and in costume.
After Ray meets Hancock for the first time, when the camera follows Ray and Mary's dog across the bedroom, what appears to be a crew member pushing the dog from behind the dresser is actually the shadow of the dog's tail on the wall. However, the dog is clearly watching something or someone behind the bed for a signal.
When Hancock throws Michel into the air, then catches him, the car in the background, which is hit by the refrigerator later, is already damaged. Only the windows are broken, and that could've been caused by flying pieces of asphalt or the concussion of Hancock's landing.
When Ray is on the train tracks, his seat belt is stuck. After Hancock flips the car, Ray is laying on the inside of the roof, with the seat belt undone. A seat belt is harder to unlatch when it has tension on it, as would be the case when hanging upside-down. Ray could have a car safety hammer, a small tool that can cut a seat belt.
In the theatrical version, Mary flies to Hancock's trailer. After Mary gets out of the trailer, the top of her SUV is visible, and Mary begins to get into it. In the next shot, Mary and Hancock stand in front of each other, and the car is gone. In the DVD version, Mary drives to Hancock's trailer.
Michel shouldn't have survived Hancock tossing him into the air. To throw Michel that high up, Hancock would have to use enough force to cause him massive internal injuries. The same thing would happen when Hancock catches Michel.
A flash explosion would not trigger a fire sprinkler. If it did, it wouldn't trigger every sprinkler in the hallway. Furthermore, modern sprinkler systems are connected to the building's fire alarm, which would've sounded.
When Mary reveals her powers, she says she and Hancock are brother and sister. They're regarded as husband and wife for the rest of the movie. The movie is hinting that Hancock and Mary are Zeus and Hera. In Greek mythology, Zeus and Hera were husband and wife, as well as brother and sister.
In the latter part of the movie, Hancock talks to Mary about the way they kissed. In the theatrical version, Mary threw him through the wall before their lips touched. The kiss is restored in the DVD version.
According to the movie's premise, Hancock and Mary become mortal and weak when they are close to each other. However, the weakness happens over time, as they spend more time together. That explains why Hancock was unfazed when Mary threw him through the wall, and why Mary was unharmed when Hancock attempted to stab her in the kitchen.
Even though both Hancock and Mary take damage throughout the movie, their clothes seem to be fine. In comics and cartoons, superheroes' protective abilities often include clothing and other items close by. Since both of them are invulnerable, it makes sense that the directors would apply that effect to prevent full nudity.
When Mary regained consciousness as Hancock distanced himself, she would've regained her gag reflex and choked on an endotracheal tube being used to maintain her airway. The device in her mouth was a Guedel or laryngeal airway, a much shorter tube that can be used in semi-conscious people to prevent tongue-swallowing.
When Hancock is dying, the paramedic shines a flashlight into Hancock's eyes. The assumption is that Hancock is unconscious, so his pupils should've been dilated. However, Hancock's pupils are fully contracted.