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.
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.