Continuity mistake: When Aquaman enters the submarine and the door knocks the guards unconscious, its position and the gun on the floor's change between shots.
Continuity mistake: When the bullies are nagging Arthur at the aquarium and the shark appears, the distance between the bullies is inconsistent between shots.
Continuity mistake: At the aquarium, the first shot shows all of the kids behind the glass, with a tall guy on the far right. When the angle changes, there's a big gap with no kids and the tall guy is gone.
Continuity mistake: Right when the guards enter the home and the walls explode, Arthur swaps between having short curly hair to it being very long and straight.
Continuity mistake: When the family is with the kid, the father reading the paper and the wall explodes, Thomas jumps to the left and covers his head with both arms. From the opposite angle, only one arm is raised, the other one is extended and on top of the newspaper.
Continuity mistake: After Thomas, the baby and Atlanna have their picture taken, Thomas is reading a newspaper. The position of his left hand is inconsistent between shots.
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.