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)
Continuity mistake: Mera takes her bracelet off, lays it on the street and smashes it. An instant later, it's in perfect shape. (01:30:37)
Continuity mistake: When the village is being destroyed, there's a bearded man with a green jacket who runs inside the church to take shelter. A couple of shots later, he is outside the church, running inside again.
Continuity mistake: Mera touches the stone where the Trident of Atlan was created with her left hand. From the opposite immediate angle, her right hand is now extended.
Continuity mistake: Mera's hair falls on her arm or not when she lies on the beach shore with the guard next to her.
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.
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.