Visible crew/equipment: When Metamorpho and Hawkgirl fly over the soldiers, stirring up a cloud of sand, the soldiers retreat backwards toward the camera. A crew member's hand suddenly enters the frame, resting on a soldier's back to stop him from colliding with the camera. While the soldiers all wear gloves and desert camouflage, the intruding hand is bare and clad in the sleeve of a black jumper. (01:42:34)
Continuity mistake: In the dark alley meeting between Jimmy Olsen and Eve Teschmacher, Sara Sampaio's hands change position on the jacket between shots a couple of times (for instance, at the end when she says "Ok" with a big sigh, her hands are under Jimmy's collar, but they were above it a moment before).
Continuity mistake: When Superman confronts Lex at his office over the dog, the background skyline changes. In the shot where the door breaks open, the camera quickly pans to the skyline and we can see one of the Liberty Plaza towers from Philadelphia. Two shots later, it has disappeared from the skyline.
Continuity mistake: The establishing shot of the post-credits scene shows the spot in bright sunlight. In the following shots, the building and wall on the left, as well as the ground, are in shadow. (02:09:00 - 02:28:21)
Continuity mistake: Superman tells the robot he's clean, and the robot raises its right hand to touch his left cheek, then lowers it. However, from the reverse angle, the hand is still on his face— and he removes it again.
Continuity mistake: When Lois and Mr. Terrific are talking outside the hall, she is standing beside the car's left tail light. In the next shot, she is a meter away by the driver's door, and in the following shot, she is back next to the tail light.
Continuity mistake: Jimmy places a sheet of paper on a tray near its lower edge, then turns to answer his phone. In the next shot, the paper has shifted to the upper edge of the tray. (00:54:52)
Continuity mistake: When the shuttle lands in Metropolis, the group steps down and Lois is two steps from the ground when Eve arrives. The shot cuts and Lois is suddenly coming out of the shuttle again, back up the steps, walking down again.
Continuity mistake: After Superman spits blood, a thick clot is visible on his lower lip. In the immediate next cut, the blood has vanished.
Continuity mistake: When Superman and Lois kiss, the strand of hair falling over her right temple suddenly appears brushed back in the next shot. (01:55:28)
Continuity mistake: During the battle at the border, a kid leans against a pole with his hand raised up to the duct tape. From the opposite angle, his hand is noticeably lower. This changes back and forth several times. (01:42:00)
Revealing mistake: When Krypto is playing with Superman, he says, "Sit! Stay!" and then Superman's left foot suddenly stretches out unnaturally, like an oversized clown shoe. (00:06:57)
Suggested correction: I'm not sure this is a valid correction, but I'm also not sure this is a valid mistake. This appears to simply be a result of the camera lens creating some minor distortion at the edge of the frame, since it only happens when his foot reaches the corner of the screen. While it looks odd, I think it's dubious and debatable whether or not this is a "mistake", and opens a can of worms where any frame distortion, even intentional, could be considered a mistake. Not my decision, though.
Apparently, the effect is either a distortion caused by the curved LED wall they used or the lens. Whatever the cause, Superman's clown-shoe look was never meant to make it on screen. This site is littered with similar issues: lens distortions, colour mismatches, faulty rear projections, and more.
