The film incarnation of Where the Wild Things Are was able to delve deeper into the examination of Max's thoughts and emotions than the book had been, and because of this provided much richer symbolism. Some elements--such as the personalities given to the Islands inhabitants--were a central focus of the film, while others, served only to support the story.
The elements of supporting symbolism, mostly introduced when Max sulks in his room, include his cardboard mountainscape and the globe which his father gave him, both of which reappear in Max's imaginary world (as Carol's--himself the primary foil for Max--elaborate and secret construction for the former, and the latter bearing an engraving that one of the inhabitants speaks to Max).
The wild things themselves--symbolizing Max's fears and general demons in the book--each carry their own symbolism in the film. The main story--which really serves only to develop Max--is that of reuniting the wild things Carol and KW who going through a difficult time because KW wants to spend time with her new friends (just as Max's sister and Mother were spending time with other people).
Each of the other wild things represents a different aspect of Max, from timid Alex to whom nobody listens and the silent sulking Bull, to violent and angry Ira and the cynical Judith. With Douglas--representing wisdom and self-awareness--Max, Carol, and KW confront the "bad guys" as he refers to the negative personas, cumulating in a head-on assault and subsequent victory of realization and determination to return home to his family which loves him.