A flash explosion would not trigger a fire sprinkler to go off; if it had, it wouldn't trigger every sprinkler in the hallway. Furthermore, modern sprinkler systems are connected to the building's fire alarm, which would have also sounded.
In the opening scenes, Hancock is shown to be drinking Seagram's 7 whiskey from a 1.75 liter ("half gallon") bottle. That product is sold in plastic bottles in the United States, and has been for many years. In fact, it's visually obvious that they are plastic bottles in the movie. Yet when the bottles are rolling on the ground, or being shattered, the sound effects indicate glass.
When Ray is on the train tracks, his seat belt is stuck. After Hancock flips the car, Ray is shown 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.
When the train comes to a halt, the freight car behind the locomotive is a gondola, but when Hancock walks around the locomotive and sees the rest of the train piling up behind it, the gondola has changed to a boxcar.
When Ray is drunk and laying on the bed talking to Hancock, he asks Hancock to help him up. In the first shot, they grab each other's forearms to for leverage. In the following shot, they are using their hands.
To throw Michel high up into the air, Hancock would have to use so much force that the boy would have suffered massive, lethal internal injuries. This is also true for when Hancock catches Michel, he would certainly not have survived.
During the shootout scene outside the bank, the bullet holes in the police cruisers are dented in as if being fire 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.
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. If you look closely, the dog is watching something/someone behind the bed for a signal.
When Hancock throws Michel in the air, then catches him, the car in the background, which is later hit by the refrigerator, is already damaged. Only the windows are broken, which could have been caused by flying pieces of asphalt or the concussion of Hancock's landing.
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 about twice as tall as everyone else, and looks like a robot or alien. It may well be a street performer, on stilts and in costume.
In the film, Mary flies to Hancock's trailer. After Mary gets out of Hancock's trailer, you see top of her SUV, and Mary begins to get into it. In the next shot, they are standing in front of each other and there's no car, as it wasn't there when Mary came. (In the DVD version, Mary is seen driving to Hancock's trailer.)
When Hancock is shot in the liquor store, the robber shoots him only once, and he is only bleeding from a single gunshot wound, however, when the TV newscaster breaks the story, she says he is suffering from multiple gunshot wounds.
When we find out that Mary has powers, she says she and Hancock are brother and sister. They are regarded as husband and wife for the rest of the movie. This is due to the movie hinting at Hancock and Mary being Zeus and Hera. In Greek mythology, Zeus and Hera were both husband and wife, and brother and sister.
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.
In the latter part of the movie, Hancock talks to Mary about the way they kissed. They never kissed in the theatrical cut; because Mary threw him through the wall before their lips touched. The kiss is restored in the DVD version.
When Mary regained consciousness as Hancock distanced himself, she would have regained her gag reflex as well, and would have choked on an endotracheal tube being used to maintain her airway. However, the device in her mouth was a much shorter tube called a Guedel or laryngeal airway, which can be used in semi-conscious people to prevent tongue-swallowing.
Even though both Hancock and Mary take damage at various points throughout the movie, their clothes seem to be fine. It is a common thing, especially in comics and cartoon, that superheroes protective abilities encompass clothing and other items in extreme close proximity to themselves (aura effect). Since both of them are invulnerable and this is a superhero movie, it would be assumed that the directors would apply this effect in the movie to prevent full nudity.
When Hancock is dying, the paramedic shines a flashlight in Hancock's eyes. The assumption is that Hancock is unconscious, so his pupils should have been dilated. However, Hancock's pupils are fully contracted.