Although the film was not released in the United Kingdom until 23 September 2005, director Hayao Miyazaki personally traveled to England in the summer of 2004 to give a private showing of the film to Diana Wynne Jones.
Howl's moving castle is actually centered around War and this is Miyazaki's main message throughout the film. However, interestingly enough, there is no mention at all of war in the novel the movie is based on.
In the novel, Sophie actually has two sisters. The second is named Martha, who is sent to be a witch's apprentice but finds a spell to change her appearance and switch with Lettie so that she can work in the bakery instead. So when Sophie goes to see "Lettie" at the beginning of the film, it should have actually been Martha in disguise. Martha is also the character that Markl falls in love with in the book.
The trivia items below may give away important plot points.
Though it's not as clear in the film, in the book Sophie is a witch herself. Each hat she makes she whispered things to or talked about the sort of person who wear it and what they would do or experience, and in the process she was unknowingly casting spells. That, along with Howl taking an interest in her, is why the Witch of the Waste came to the shop. Notice how the Witch scoffs very particularly at the hats.
Sophie is established as a witch who can talk life into things in the book, while in the movie it is left up to the viewer to realize this. Some of the moments that make her powers obvious are when Sophie rescues the scarecrow and he gets deeply attached to her, as well as when her hair gives Calcifer extraordinary strength even while Howl is absent. Calcifer repeatedly singles her out, confirming that only if it is her performing the action, will he be able to live on and Howl be able accept his heart back. Sophie is able to keep Howl's heart and Calcifer alive through her inherent powers. Sophie, being a witch, also has significant power over the Witch's curse, only she doesn't know about it. In her sleep, while she is dreaming, and during deeply emotional moments, when she is upset or happy and completely in love with Howl, she turns back into her younger self, being able to undo the curse by accepting and embracing herself, giving in to her own powers.
Symbols and metaphors are rampant in this story. The Castle is representative of Howl himself, a highly powerful yet disorganized mess, with a lot of baggage. The black gateway on the portal/dial is the way to Howl's psyche and unconscious, which he keeps himself immersed in. Calcifer, the fire, is of course the heart, quite literally. Markl could be understood as the innocent childlike part of Howl. Sophie starts by organizing things in the Castle, wins over Markl, as well as Calcifer. At the end, she is able to help Howl finally when the ring Howl gave her leads her to his innermost self, the black gateway on the dial.She visits his past, and finally is able to help him reconcile his past, his feelings(his heart) to his present state.