Continuity mistake: After Arthur puts his father in the truck after the bar, we see Mera emerging from the water from the left of screen, right of the truck, off to the side casually walking up. When the camera changes we hear a splash and suddenly Mera is on the dock behind the truck dripping water. This is showing that she was walking up from the side, suddenly went back into the water, only to jump back out again at a different spot on the dock.
Factual error: Aquaman lifts a submerged submarine towards the surface, which should start to sink again straight after releasing it, as its ballast tanks are still full of water. It shouldn't stay floating like that.
Continuity mistake: When Black Manta gets the gold coins from the Atlantians the bag falls in front of him but in the next shot the bag is behind his feet.
Continuity mistake: While Arthur as 16 year old trains with Vulko he falls into the water and gets his back wet, but in the next shot the shirt is dry.
Continuity mistake: After Aquaman saves the Russian sub the soldiers get out of the hatch, but he broke it when he first entered.
Continuity mistake: While Atlanna is hugging Arthur before the Atlantian soldiers come for her, the kid is different between shots, even the hair changes style.
Deliberate mistake: Spoilers! When Black Manta is defeated, he is knocked unconscious and tumbles down a rock face after his helmet explodes on his face into the waters by the shores of Sicily. These currents and waves at best would have carried him to the rocks or the beach, leaving him on land or near it. However in the after credit scene he's somehow found out in the middle of the ocean on a broken drift wood. He would not have been carried back out to sea like that.
Suggested correction: The water is tidal. If the tide was going out, the current would take him out to sea.
There are hardly any tides in the Mediterranean Sea http://scienceline.ucsb.edu/getkey.php?key=995.
Factual error: An M203 round arms at between 14 and 27 meters, and produces a ground burst that causes casualties within a 130-meter radius, and has a kill radius of 5 meters. Even if it did work all Manta and his father would have been killed. (00:18:35)
Factual error: Atlantis was in the Sahara when it was still an ocean, that was about 4000-8000 years. But part of the riddle was to find the king, Romulus. Rome was founded around 750 BC. So no way for him to know where they would build a statue about someone that wasn't born yet.
Continuity mistake: Near the end, during the final combat scene between Aquaman and King Orm, the gigantic whirling propeller blades in the background noticeably change rotation rate: At the start of the battle, the blades are turning rather lazily; but at the height of the battle, the blades are spinning rapidly, a virtual blur in close-up shots, drawing a steady stream of sparks from Orm's helmet when it touches the propeller. When Aquaman defeats Orm moments later (and their mother, Queen Atlanna, appears), the huge blades are spinning slowly again. I'm not talking about during dramatic slo-mo action effects, but during the normal-speed action. (02:04:50 - 02:07:10)
Factual error: When Jesse shoots the M203 round at Aquaman, the distance is too short for it to arm and explode. (00:19:40)
Continuity mistake: Before the guards break into the house where the family is with the kid, the front shots show the dog unease. Right before he barks, from an angle from behind he swaps to relaxed. A shot later, from a front shot, the dog swaps back to alert and barking.
Continuity mistake: When the family is about to have their picture taken, Atlanna is holding the baby's head. A shot later, her hand is around his body.
Other mistake: When Tom picks up Atlanna when she washes up, she's unconscious, but she's able to hold on to her trident.
Suggested correction: It is emphasized that she is still holding it even when unconscious.
Continuity mistake: While Arthur as a 9 year old is training with Vulko the sun changes between shots.
Other mistake: Artistic license via CGI physics is taken for all the characters in the water to keep their hair from ever flowing over their faces, no matter how long or how the currents might affect their hairstyles. When characters emerge out of the water, their hair remains nearly unaffected.
Continuity mistake: Before Atlanna throws the trident at the TV she holds it differently between shots.
Continuity mistake: After Aquaman drinks his first beer with his father, the handle of the jar swaps from facing a 9 o'clock to a 7 o'clock position.
Continuity mistake: At the aquarium, when the bullies arrive there's a woman with a yellow jacket behind them. She disappears in the angles from behind, and reappears in the ones shot from the front.
Continuity mistake: When Aquaman picks up the bottle containing a map in the Sahara, he is originally holding the bottle from the bottom while starting to unravel the map. The view cuts unravelling the map from his POV, and he is suddenly holding the bottle from the top. (01:21:29 - 01:23:19)
