Lectitans posed the question What does it mean to have a "thorough knowledge of children's literature"? and I've been thinking about it for several days. Other people have left their answers in the comments to the question or in their blogs.
It means to not think that your childhood reading was universal. No matter what type of reading you did, at best you read a fraction of the books out there. My friend Carlie says, "the plural of anecdotes is not evidence," and that has become my mantra, including drawing any conclusions from my own reading history and habits.
It means not relying on library school classes. Yes, the classes are valuable, no two ways about it. The value is in the titles read; the professional journals you are introduced to; the passionate discussions about books. Here's one thing about books; every reader has a different experience with a book. If you think your reading is the only one of value... or the only proper way to interpret a book... see above about the plural of anecdotes. If you hated a certain book or genre -- and others loved it -- as a library professional, you cannot let your hatred or dislike stand between that book / genre and the young readers you will be working with. A library school class will force you to read books you wouldn't have otherwise and to listen to the opinions of others. It is also extremely valuable to read the literary criticism and articles about children's literature; so you really "get" to the heart of what makes a book good. The problem with a library school class -- assuming that's all you need to "know" children's literature. It's just the start.
Read a lot of books. Read books that you wouldn't normally read. If you "never" read fantasy, try a few.
As a librarian, listen to what your patrons read -- and read the books they say they love. Readers Advisory works both ways.
Respect all readers... so be aware of that as you look at titles. Some first graders may be reading Harry Potter; others are not. If you only value the HP readers / reading experience, you are doing a disservice to the other readers; and guess what? They know it. And by not having the knowledge of great, fun books for the non HP'ers, the readers who aren't reading above grade level, you may risk turning them off reading forever. So as you read, and read about, books, try to think of the many types of readers out there.
Read professional reviews of current children's literature. Read blogs, too. Lurk at listservs. Read the award winning lists. (Note: I mean be aware of the winners and titles on lists; not to read each and every book.) In other words, build a general awareness of the books that are out there -- it is impossible for even the fastest reader to read everything. And frankly, a dislike of fantasy (which is OK!) shouldn't stop a librarian from being able to recommend titles to a fantasy lover. The "work around" not reading fantasy is staying up to date on what fantasy books are out there.
Add depth to your knowledge. Which means, look towards older books and try to gain the same knowledge and awareness of them as you do the current books. Blogs are helpful for this, because older titles are reviewed. But there are helpful books, also. I have every The Best in Children's Books (edited by Zena Sutherland) going back to 1966-1972. While some of the books are now out of print, others aren't; and you'd be surprised how many of these older books are either stumper titles or books that parents want to share with kids. (And it's kind of fun to skim these Best of ... books to see what "made it" as a classic that is still around, what sounds just like that "new" book that everyone says is so "original.)
OK, so maybe going too far back is a bit unrealistic with books being out of print; but you MUST have depth to your reading. I cringe when I hear of some of the books and authors that librarians "draw blanks" on books like Tom's Midnight Garden. A person should at least recognize the titles of these older classics. Children's books have been published for a long, long time; do not fall into the belief that the only good books are the newer books. Because it's easier to keep up on new books, or to read just older books, and to think being a reader at age 10 means you "know" the older titles, this depth of information is often overlooked. And yes, it's harder to acquire this depth because many of the print journals only review new books and some libraries discard the older reference works such as The Best in Children's Books (links above).
Links to people answering this question: Bri Meets Book; will add more as I find them.