Today I explored Flash AS3.0 debugging and it is awesome. Flash debugger is an extremely useful tool for serious programmers and for kids too. Using this tool debugging ActionScript becomes two times simplier and much more in some cases. I present here mostly links to the info.

Basic info about Flash debugger
http://help.adobe.com/en_US/Flash/10.0_UsingFlash/WSD76536C2-C8AA-472a-BE2F-BD0D0855972Aa.html

Understanding ActionScript 3 debugging in Flash
http://www.adobe.com/devnet/flash/articles/flcs4_as3_debugging.html

Introducing the ActionScript 3.0 debugger
http://www.adobe.com/devnet/flash/articles/as3_debugger.html
part 2
http://www.adobe.com/devnet/flash/articles/as3_debugger_02.html

And some more info about an external debugging tool
http://gotoandlearn.com/play?id=109

Notice that this article is dedicated to debugging in Flash authoring tool. Debugging in Flex or other ActionScript editors may differ.