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: 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: 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: 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: 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.
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.
Other mistake: While Thomas lifts Atlanna she is unconscious but she is still holding the trident with her left hand.
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.
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: 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.
Revealing mistake: When Orm presents the weapons to Manta as a water hologram, Manta walks right through the hologram with half of his body. This arm passes through the hologram made of water and even makes a splash sound. However, there is not a single drop of water on Manta's completely dry clothing after this.
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.