When Damiel meets Falk at the hot dog stand, the amount of coffee in Falks cup increases between shots.
The position of the trapeze artists' arms change after Damiel stands in her trailer.
The position of the boys' jump-ball changes as Damiel passes by.
When Damiel meets Falk at the hot dog stand, the time of day shifts during the scene. Damiel is seen a dull and gray day. Falk is seen in sharp artificial light with a dark window behind him, typical for a night shot.
Upon waking Damiel is hit by a cuirass presumably thrown from the helicopter he sees above. If a 10 pound piece of armor was dropped by a helicopter at 100 feet it would exert over 635 pounds of force on Damiel, more than the 520 necessary to crush his skull. Even if it doesn't hit him directly it would hurt him much more than it appears to.
When Cassiel sees Damiel's footprints in the sand just after he becomes 'real' the prints shown are too far apart and the foot angle too extreme to be anything like the normal walking gait they had up to that point.
When Cassiel (Otto Sander) is crossing the street, a bus slows down to allow him to cross the road, then accelerates once he's clear. As Cassiel is an invisible angel, the bus driver shouldn't have been able to see him.
The end credits that list who played the angels in the library has them credited as "The Angles".
After Damiel becomes human, he buys a cup of coffee at a food stand. The proprietor pours coffee into a plastic cup, and Damiel immediately takes a large gulp - neither of which would be possible if the coffee were hot, as it would be if it were freshly poured.
When Damiel rides the subway, the train passes a station without stopping. There are fresh posters on the station wall so this is not one of the "ghost stations" where trains did not stop in the 1980s.
When Marion enters her caravan and undresses, the "sun" is shining on her body from east and west at the same time.
In one of the earlier shots when the camera flies around the Berlin sky, the shadow of the helicopter can be seen in the clouds below.
In one of the opening shots where the camera circles a tower, more like a radio transmitting one, the spinning helicopter blades can be seen at the top of the frame
During a montage sequence involving fast-forward, blurry movements, one shot shows a man passed out by the phone booth. The camera's shadow becomes visible on the left side of the booth.