These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fridge Brilliance: Ponyo was told by her father that she can't work magic and stay human. Remember that when she casts spells, she takes on that weird appearance that looks like a tadpole or a chicken. Or a vaguely anthropomorphic Tiktaalik.
Ear Worm: The theme song. Partially due to the presence of certain siblings of certain controversial Disney personalities. But even if you hate the song, it's undeniably catchy... which makes it much more of an Ear Worm if you do hate it.
Painful Rhyme: "She's a little fish from the deep blue sea" / "She's a little girl with a round tum-MY."
Ensemble Darkhorse: Fujimoto. Despite (or even because of) the fact that he's a henpecked, crotchety, and overprotective father, two-thirds of the small but growing fanwork base involves him.
You could also say that it's because he's an adorable Cloudcuckoolander and overprotective but loving father.
Or because he has a mostly untouched backstory as a former human who became an undying sorcerer of the sea.
Or because he's funny as hell.
Or just that he can be creepy and adorkable at the same time (at least in the English dub, since some of it has to do with his voice). For instance: "Respect your father!" (said menacingly, the creeper part) -> essentially a pratfall (dorky) -> "Girls, I'm trying to save your sister!" (said pleadingly/worriedly, kinda cute as a protective dad thing).
Harsher in Hindsight: The 2011 8.9 earthquake had the ocean sweeping over elevated roads in the same fashion as the film. Nobody dying, and everyone shrugging it off as a 2.0 earthquake? ....yeeeeeeeeeaah.... not really.
Uncanny Valley: Granmanmare evokes this due to her design being slightly more realistic than the traditionally Miyazaki-esque characters that surround her.
Also, Ponyo's inbetween human-and-fish form.
Values Dissonance: Leaving five-year-old children alone and unsupervised (in the middle of a typhoon, no less!) could be considered criminal neglect in some jurisdictions. Still, it can be considered as Lisa choosing the lesser of two evils — either bring them with her where they'd all easily be swept away by a particularly bad wave, or let them stay on high ground in the comparatively safe house.
Why isn't staying at home an option? Did the old people at the retirement home at least give her a light lecture? They've lived a full life, but if anything happens to Lisa, or her husband at sea during the typhoon, the two kids wouldn't last long.
The reason why she left them to go to the retirement home may have been the movie's way of reflecting the Japanese value that the young should take care of the elderly, no matter the circumstances. A strong case of Value Dissonance, especially since in Western culture it's viewed as the other way around.