(at around 60 mins) After John Murdoch opens the door and almost falls from the building, as he hangs by his hands the door is on his left, except when shown from above, when it is on his right.
(at around 17 mins) When Murdoch is on the Shell Beach billboard and collapses after reading the newspaper clippings he found in his coat pocket, a stranger appears/disappears/reappears on the steps in the background.
(at around 1h 8 mins) When the doctor is pointing a gun at Murdoch and trying to give him the injection containing his memories, it is daylight outside through the windows behind them, but there is supposed to be no daylight.
(at around 18 mins) Mr. Quick meets his death when the waving arm of the Shell Beach billboard chops his skullcap off, leaving the waving arm hanging to the left of the other arm. In following close-ups, the waving arm is missing.
(at around 59 mins) When on the fire escape, one of the Strangers opens the window and enters the building. In the next shot, all three Strangers are still on the fire escape.
(at around 57 mins) Although when John Murdoch jumps across the roofs, he jumps onto the same roof twice, in this city it's quite possible for there to be two identical roofs.
(at around 1h 5 mins) When the glass partition is broken, a second sheet of glass is used to protect Jennifer Connelly. At slow speeds, John's hand is clearly visible reflected in this safety glass.
In the opening scenes of the film, the elevated train is very obviously seen to be a model by the way it moves, and the model people inside bounce around.
The wire that pulls the stranger up on the roof in front of John is clearly visible for a moment.
(at around 60 mins) After John Murdoch opens the door and almost falls from the building, he grabs the ledge and slams into the side of the building. The building bends in with John's impact.
At 1:19 the syringe prop has no needle attached.
(at around 7 mins) The band playing in the beginning has an upright bass-player, but the sound is clearly that of an electric bass-guitar. The playing style is also not true to an upright. The sliding note might give this impression, but the other notes are simply too light-touched to be an upright.
(at around 7 mins) John Murdoch's wife sings in a club toward the beginning of the film. Though her lyrics match lip movement, the rest of the band is out of sync (drums, bass, etc.).
(at around 60 mins) The cable supporting John Murdoch when he opens the door and nearly falls down the shaft.
(at around 60 mins) The cable holding John Murdoch when he jumps from the doorway to the building when being bitten by Mr. Sleep.
(at around 31 mins) The cable holding the doctor while he is being levitated by the stranger is clearly visible as he lands.
The Strangers are supposed to have a collective memory, but when Mr Hand gets injected with John's memories, that package isn't shared among them.
When the Goodwin's dining table expands, serving dishes appear, so why not the candelabras as well?