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: 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: 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: When Aquaman and Ocean Master were trident fighting their second round on top of the ship, Ocean Master ripped off a part of the ship and threw it at Aquaman, but then the hole Ocean Master made was just gone. When Ocean Master used his trident to rip across the ship's roof to stop Aquaman from pushing and stood up, again the damage was just gone. (02:04:50 - 02:05:30)
Continuity mistake: Aquaman asks Mera what her name is while a strand of hair runs along his forehead. A shot later, it's gone.
Continuity mistake: When Aquaman watches the news talking about him and the submarine, his left hand swaps between being around the beer glass or not, depending on the shot.
Continuity mistake: After the submarine scene, Aquaman shows up on the pier. Check the wooden plank on the right, and you'll see that the puddle changes size three times between instant cuts.
Continuity mistake: In Italy, Mera fights against a guard, who crashes against a bottle cabinet, causing several bottles to fall. A shot later, the bottles are back in place.
Continuity mistake: Atlanna hugs Orb, her left hand over his shoulder. Then she places it on his chest and says, "Arthur saved me." An instant cut later, her hand is back on his shoulder.
Continuity mistake: After Tom suggests naming the baby Arthur, Atlanna holds his head. An instant cut later, her hand is along the baby's back.
Continuity mistake: Tom introduces himself after Atlanna does, who is holding her mug with both hands overlapped. An instant cut later, her hands are apart.
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)
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.