In the movie when James and the bugs are able to breath underwater it seems strange at first until you remember that they all injected magic crocodile tongues that transform them. It also explains how the centipede was able to single handedly take on the whole skeleton crew.
Why is it that the other bugs and James are so ready to believe that the Centipede is the world-traveling adventurer he says he is? He's the only non-European among them—as an American insect among Europeans, he's already the one most likely to have traveled the farthest out of all of them.
The same magic that makes James' wishes come true - traveling to New York, having a large group of friends that also act as a caring, surrogate family - also brings to life his fears. The mechanical shark spits out the same plates of disgusting fish heads Spiker and Sponge fed him, and threatens to prevent his escape to a better life just as they do in the film's conclusion.
It seems a bit random to have a musical number about all the weird things the bugs have eaten, but it becomes Fridge-Heartwarming when one realizes it's a bonding moment between James and the bugs. James knows what it means to have nothing but gross food, like those fish heads his aunts served him. The bugs are sharing what they've had before, and it's no better. And the song is concluded by both James and the Bugs' mutual understanding that good food (namely the peach) is something to be very grateful for.
What's more, the bugs most likely have had their fair share of eating less-than-great food, because of how Spiker and Sponge's garden is relatively a barren wasteland for them.
As a young child, one wonders why the police officer is particularly livid when he orders the crane driver to take Spiker and Sponge out of his sight. Is it the wigs? Is it that they were lying? Not particularly. It rather has to do with him coming to the (in-universe) Fridge Horror that if James was telling the truth about magic and the giant bugs, then perhaps he was honest when he told everybody Spiker and Sponge abused him, physically and verbally and emotionally. He's not simply disgusted that these two scumbags lied to his face, the police officer is outraged at these two for trying to take back a child they were going to hurt some more. Which makes it all the more satisfying when he orders "Get these two creeps OUT OF HERE!!"
Also, when James first meets the bugs in the film, only Miss Spider knows his real name (the others didn't know, or thought that his aunts' nicknames for him were his name.) It might be overlooked - however, when you find out that James befriended Miss Spider and saved her from his aunts in the beginning it makes sense that she knows his name. She would have heard his "I Am" Song, after all.
When James has his nightmare about his aunts chasing him down, he wakes up to find the peach drifted far into the icy Arctic. While it may not be intentional, science has proven a link between nightmares and sleeping conditions—scientifically speaking, sleeping in a cold room is more likely to make you have a nightmare.
James was quite obviously traumatized by the fact that his parents were gored to death by a rhinoceros when he was younger, so it would make sense that The Movie would manifest his fears into the Eldritch Abomination of a giant sky rhino from nowhere.
In the book, film, and musical, James is willing to risk his life to help Centipede (he falls off the peach in both the book and musical and goes after a compass in the film) despite being a young child. Why? Because he's already lost his mother and father and doesn't want another family member to die.
It might seem a little odd that in the book, James was the only one to go after Centipede when he falls into the ocean. However, there is a very good reason: James is the ONLY one in the group who can swim. In the film, Miss Spider goes because she's a Mama Bear through and through, and she has her string as a safety line.
The film version's Downer Beginning shows James and his parents on a beach. If this is was in fact a beach home (permanent or just a summer getaway spot), it's likely that James learned to swim sometime before tragedy struck.
The police in New York City opted to tell the crowd to flee while not racing to the aunts to stop them from murdering James. To be fair of them, there were just a few seconds between the aunts' Villainous Breakdown/Moral Event Horizon, and the bugs coming down to attack them. Any longer, and the police would've shot the aunts dead, saving James and probably everyone in New York. They just needed to get people out of the way first in case of stray bullets, and James was at a safe distance from his monster aunts to give the police enough time to shoot them.
When the giant peach impales itself on the Empire State Building, James was inside. He's lucky he didn't get stabbed, too!
And on that note, what do you think the bugs were thinking when the peach fell? As far as they knew, the little boy they loved as their own could very well be seriously hurt or dead. One can only imagine that they were beyond relieved when they were all reunited, but still. There is a reason why they call out for him when they land, obviously relieved they he's (relatively) unharmed.
A bit of rather sad Truth in Television. Notice that when James first meets the bugs in the peach, he tends to shy away or tense up when they get close. Why? Because he's used to being beaten by his aunts and is afraid that these strange adult figures might hit him like his aunts do, which is typical behavior for an abused child. However, this behavior vanishes as the movie goes on, showing that James has come to trust his new friends and knows they'd never hurt him.
He also pleads for the bugs not to eat him... which makes sense given his Aunts constantly used his trauma of the rhino causing his parents' death as a threat. In other words, he might have instinctively thought any strange creature he encountered would do the same to him.
In the film, Miss Spider mentions that she never had any friends before meeting James; according to her, it's because bugs naturally fear her. While that probably is the case, it should also be noted that she lived in Aunt Sponge and Aunt Spiker's house. Both of them despised bugs and killed any that they saw; hell, they even tried to kill her. It's likely that even if Miss Spider had met bugs that were friendly to her, they were killed by the aunts shortly after.
If the aunts killed James, accidentally or otherwise, no-one would ever know. They're completely isolated up there and the aunts didn't let James out while the sightseers were present, so it's very likely that no one even knows there's a little boy on that hill.
They're his legal guardians, so presumably, there's some government record somewhere that they're in charge of taking care of him. That said, by the time any official began raising eyebrows, it'd be too late for any lingering evidence to matter, and in absence of other witnesses, any plausible alibi by the aunts would likely be accepted.
In fact, the film adaptation confirms this. When the aunts explain to the beat cop in New York City that James is their ward and the peach is theirs, they provide (soaked) legal documentation to prove this. This is indeed why James was at risk of returning home to England with Sponge and Spiker (before their Villainous Breakdowneffectively proved his accusations of abuse right).
In the book, considering Aunt Sponge and Spiker died, British Social Services don't account for James's disappearance. They might have assumed he either ran away during the chaos and what remained of the shack would show evidence of child abuse (which is what happened in The Sandman) or that he got killed and is Buried Alive somewhere.
