Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person Omniscient
At first the narrative perspective of Howl's Moving Castle seems like your standard third-person, all-knowing point of view. The narrator has no name and plays no direct part in the plot, but it has total access to the thoughts and feelings of the characters, and especially our main character Sophie. Yet when we started thinking about the narrator in a bit more depth, we realized that actually we've got a pretty unusual one on our hands.
See the narrator is always filling us in on the actions of the characters. We also know when the characters (and again, especially Sophie, since she is the main focus of the narrative) are having sudden, strong feelings. But the narrator rarely fills us in on the characters' views on why they're having their feelings. The characters in Howl's Moving Castle are really emotional, but the narrator generally leaves it up to us to figure out why they react the way they do.
A great example of this show-don't-tell narrative style appears when Sophie and Howl are bickering particularly strongly after Howl discovers the dog-man's curse. Sophie is extremely grouchy and has been ever since Miss Angorian made an unexpected visit to the moving castle. When Howl starts yelling at her for not mentioning the dog-man's enchantment, Sophie is glad because now she can get into the fight she really wants. When Howl suddenly seems to lose his anger, Sophie keeps going:
Though that seemed to mean Howl was no longer angry, Sophie found she was angrier than ever. She stumped off into the shop, where she banged about, shutting the shop and putting things away for the night. She went to look at her daffodils. Something had gone horribly wrong with them. They were wet brown things trailing out of a bucket full of the most poisonous-smelling liquid she had ever come across. (19.42)
Here the narrator tells what Sophie's emotions are: she's "angrier than ever." And the narrator also shows us the results of Sophie's anger: the daffodils she was trying to grow have produced "the most poisonous-smelling liquid she had ever come across." Her emotions affect her magic and they affect her mood.
But the book never actually says something like Sophie realizes that she is feeling angry because she has feelings for Howl that she can't deal with—we have to put together the clues. It's up to us to figure out that the sudden appearance of Miss Angorian in the castle + Sophie's certainty that Howl is trying to date Miss Angorian + Sophie's insecurity about her appearance as an old and a young woman = intense jealousy and rage at Howl.
The narrator tells us just enough to give us clues about the characters' feelings without always explicitly leading us through their thought processes. And this process of thinking through the characters' reactions makes us put ourselves in their shoes imaginatively, which means that we feel even closer to the fictional people Diana Wynne Jones presents to us.