Perhaps the triple-click shortcut is turned off for some reason, though a quick search indicated that it was on by default in iOS 6 and 7. Normally double-click is enough to show all running apps.
You could check in Settings -> General -> Accessibility -> Accessibility Shortcut.
You're right, it was turned off. I do need to select text first. This makes it not very usefull for iBook ebooks. You' like continues reading. Oh well, audio books for now.
If you need to select text, something still isn't working properly. You should be able to drag two fingers down from the top of the screen, and it will read and turn pages for you until the end of the book.
You could check in Settings -> General -> Accessibility -> Accessibility Shortcut.