Usage like that is fine on the canvas page, but not allowed on the profile and homepage. One way around it is to put the entire contents of mootools.js into a <script> tag on the profile and homepage surfaces. However, this is pretty messy.
Do you really need mootools on the canvas and homepage? Most apps have a very simple homepage/profile surface, they just grab data from a remote server via makeRequest(), and display it. Consider using "plain" JavaScript for the profile surface, it makes it less bulky and quicker to load (which is important for people with lots of apps).