Read through the book in its entirety, focusing solely on the words themselves. If possible, have someone cover the images with sticky notes before you start reading; otherwise, do your best to ignore the images or move past them quickly.
Apply standard literary analysis to the text. Evaluate the strength of the story, the development of the characters and the way it pulls you along from one page to the next. On a more technical level, look at the rhythm and syncopation of the language, the structure of the prose and the way the story is organized. Pay particular attention to the page breaks, noting where the text stops and when it picks up again. That plays a huge role in the story's overall pacing.
Examine the book again, this time focusing primarily on the illustrations. Examine them closely while skimming over or ignoring the text, focusing on the relative merits of the illustrations as art. Look at the overall composition of each image, the way it draws the eye to certain details and the particular combinations of color, if applicable. Study the stylistic choices the artist made and see if they hang together from picture to picture.
Go through the book a third time, this time paying attention to the way the images and text interact. Look at the passages which the artist choose to illustrate and the way he interpreted the writer's words. See if the images complement the text, whether they're placed on the same page and how they accentuate the action in the prose. Watch their physical placement in the book and recognize the ways they break up the text. A good picture book should feel totally organic, with each half complementing the other. A mediocre picture book feels more disjointed, struggling to integrate its disparate elements.