** NOTE **
The principal requirements are that (1) it is possible to inspect objects to see what references they have, and (2) that changes to references can be detected.
These requirements are met: (1) is achieved by inspecting the properties and (2) is met by using aspects to monitor changes in the properties; for private references, this can also be met by using custom "inspectors" that can see inside the classes and react to changes.
This is relatively trivial for new class heirarchies (and GC by default only operates on explicitly nominated classes heirachies), but retrofitting to existing class heirarchies needs to be done with some care; adding in inspector classes for private members has it's implications too.
IMHO there is an argument that GC would be most useful if it could navigate qx.ui.core.Widget and while I've attempted to do this it's not complete and is proving hard to debug some of the problems which have cropped up - the current version of Chrome gets a stack overflow and becomes unstable and Firefox's debugger is unable to debug during startup (which is not GC related). I think that this is caused by exceptions due to calling getXxxx on properties that are not yet initialised, but I have run out of time to take this further.
When Qooxdoo objects are no longer needed it is typically necessary to call dispose() on unwanted objects to release their resources; not tracking objects and dispose()ing of them can lead to memory and other resource leaks. The Qx-GC contrib automatically tracks references to objects and dispose()'s of them when they are no longer needed, simplifying code and reducing the amount of testing and debugging work needed to be done.
As important as it is to keep track of what's in use (and what's not) doesn't make it easy to do; in fact, for anything but the most straightforward of applications, keeping track of resources can become a challenge, and like all challenges need testing and debugging.
Garbage collection is a neat and simple concept where the language silently takes care of cleaning up unused objects for you; in Javascript this is automatic and is built in to the language, but this only works if you don't care when an object is no longer needed. Like many frameworks, Qooxdoo does care and every object must have it's dispose() method called when the object is no longer needed.
Languages with built-in garbage collectors often include Weak References, IE a reference to an object which becomes null when nothing else refers to the object; this is most often used for caching mechanisms, where something is kept around (in the cache) only while other code needs it. Javascript does not support this - but Qx-GC does with the com.zenesis.gc.WeakRef class.
Please see the Qooxdoo contrib site for documentation:
http://qooxdoo.org/contrib/project/qx-gc