How to glean info from a message that simply has the letters shuffled? Suppose someone had published a several hundred page (sensitive) book, but had randomized all of the letters in an order known only to them (e.g. with a vector of random numbers of the same length as the book's characters).

This initially strikes me as relatively riskier than something of comparable simplicity (like a one time pad) since the letters are all in the clear.  But, I can't quite see how an attacker would benefit much from that information.  Are there known attacks on this sort of thing to learn things about the text?  What could be learned?  Could one maybe at least tease out an idea of what the book was about?  At what message lengths (if not all) could it be a big problem?

Hopefully this doesn't qualify as asking the community for "peer review of a cryptographic scheme"!
What you are describing is called a transposition cipher. 

First of all, it would be easy to detect which method you are using since the frequency distribution of your cipher text will be the same as the language of the plain text.

I think the biggest problem with using only transposition as opposed to a combination of both substitution and transposition is that you do not need to manipulate the whole message in order to find the key (i.e the order in which you shuffled it) finding how one word was shuffled reveals how the whole plain text was shuffled.

Another weakness is that even if you do not have the correct key, being close to it already reveals a lot of information.

A way to break this cipher would be to take a small chunk of cipher text and shuffle it around until you find some anagram to a known word, then solve the anagram. 

Edit :

After rereading the question, if you were to shuffle your text randomly as you said in your example it is similar to using a one time pad for the exception that the key to the pad would be draw from a different distribution since you probably will not have equal amounts of each letter of the alphabet in your book.

Let $m$ be the book and $c$ be the shuffled book you can derive a key $k$ such that $|k| = |m|$ and $m\oplus k = c$.

$k = m\oplus c$.