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.
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.
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: 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)
Continuity mistake: The goldfish bowl is pointing length ways, but when Kidman is laid on the couch the fish tank has changed direction completely. (02:24:00 - 02:34:00)
Other mistake: When Arthur meets Atlanna on the beach, she steps towards him. When the camera zooms out, there are no footprints in the sand.
Other mistake: During the final battle between Aquaman and king Orm, notice the propellers, both left and right prop rotate in the same direction, however the physical lay-out of the propellers are not matching (mirrored), thus one prop would give forward thrust, the other will give rear thrust. Not logical with both rotating in the same direction.
Other mistake: Aquaman and the princess were in Italy, then they are on a boat, but there is no great deep trench in the Mediterranean, and they couldn't have made it to the Atlantic in that fishing boat.
