Well, Apple Support wrote to me "please make sure that your book doesn't contain any emoticons or unicode".
It seems crazy for them to write that without some more detailed pointers. As it says in the evernoor link "Tip #2: Make sure all your files are either UTF-8 or UTF-16 encoded. " That is Unicode. iBooks accepts books in almost all languages, which is only possible with Unicode, and the epub standard also requires Unicode. It is unfortunate if Apple Support is really so clueless on this subject.
One place where Unicode might trip you up is in urls contained in the text, or in chapter titles if these become file names. Have you used any Greek or other non-ascii characters in these perhaps?
I'd be happy to have a look at your book if you have a place to upload it or if it is not too large to email.
Have a look at https://discussions.apple.com/message/21708274#21708274
I had one 'invalid character', a bad tau character I found by trial and error.