Continuity mistake: When Melody is in her room getting ready for her party, at one shot her hair is down. In the next shot of her, it's in a ponytail, and in the next it's down again.
Continuity mistake: When Morgana traps melody in the cavern, Flounder is seen in his younger size. The next time Flounder is seen he is back in his adult size.
Continuity mistake: When Morgana sinks Prince Eric's ship, he asks where Melody is and draws his sword. When Cloak and Dagger (the manta rays) pull him under the water, he no longer has his sword in his hand.
Continuity mistake: When Melody is singing for a moment, as she rises out of the sea on that huge whale, her green ribbon is missing.
Answer: King of the Sea does not mean psychic powers that allow him to be able to snuff out everyone's location. Only power he has is through the trident, which obviously cannot pinpoint location as he couldn't find Ariel when she was missing. It's likely the humans have no idea of the family's mermaid history, because yes, the snotty kids probably would have greatly teased Melody for it.