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: 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)
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)
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: While Atlanna is hugging Arthur before the Atlantian soldiers come for her, the kid is different between shots, even the hair changes style.
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: 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.
Continuity mistake: While Arthur as a 9 year old is training with Vulko the sun changes between shots.
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.
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: In Sicily, the lorry that brings Mera and Aquaman drives way past a terrace umbrella towards a street. When the shot changes, the lorry comes to a stop several meters behind, next to the terrace umbrella.
Continuity mistake: Before Mera eats the roses, two backpackers, one with a pink T-shirt, walk by and head towards a street. When the shot changes they've moved several meters back and are walking behind Mera again.
Continuity mistake: In Sicily, three women are having lunch by the florist stall, the one with sunglasses sitting in the middle. Two seconds later she's now sitting on the right side, and also the man behind her has disappeared.
Continuity mistake: In Sicily Mera eats the roses and puts her right hand to her mouth. From the opposite angle her arm is down.
Continuity mistake: When Atlanna is found by Thomas, the trident by her face changes position between shots.
Continuity mistake: At the bar, when the bullies ask Aquaman if he's the fish boy from TV, he faces to the right. Angle changes and he's now facing straight, only to repeat the movement.
Answer: Because what they're looking for is in the ocean. The maps, the ancient texts and markers leading to the trident. It would seem odd to search for Arthur on land then return to the ocean.