In the past we recommended an excellent EPUB3 checker that gets frequent updates and offers a convenient user interface:
http://www.pagina-online.de/produkte/epub-checker/
In normal use, you simply drag the ePub file onto the main check screen - and after a few seconds you get the check results (hopefully the screen will be entirely green and declare 0 problems in the book).
But there's more - you can simply drag into the screen the folder that contains all the files of your book, with no need to package it at all!
Not only will the book be checked and give you a result as usual, but the software will also package the book for you correctly. Completely worth it! And it saves you the problems of packaging with various zip programs, which will usually lead to a "MIMETYPE" problem where it isn't in the right place in the packaged file.
