I don't remember reading this book for myself, although it certainly has been around long enough. I do, however, remember reading this book to one of my younger siblings, probably my younger sister. Anyway, today I read it to my almost-five-year-old son for the first time.
My son wasn't at all anxious about the monster at the end of the book. He kept pointing to Grover and saying "That's a monster!" So the ending did not surprise him at all, although it did make him laugh. I don't remember how my sibling reacted when I read it to her (or him), but I'm pretty sure it was pretty close to my son's reaction. Despite the "monster" in the title, there is nothing frightening about this book. And that is a very good thing. It's also a very good thing if we learn to laugh at our "monsters".