We've been having fun with some high-minded literary analysis, but remember that Corduroy is written for very young children. They can understand and follow along with a story, but in their minds, whoever is reading the story is the one who's telling it. The concept of perspective is still a few years beyond their grasp, so the omniscient third person narrator works well for this book.
For the most part, the narrator follows Corduroy around, describing his actions to the reader. However, there are a few instances where the narrator knows something Corduroy doesn't, like the fact that his mountain is actually an escalator or that the night watchman is making rounds in the store.
In our experience, these moments are always a big hit with toddlers, who love being "in on the secret" so much they might even forget it's almost time for B-E-D.