When using FlashDevelop and having multiple embedded swf files, the debugging of the Flash IDE is not enough.

I've tried using ThunderBoltAS3 at first, and found it quite helpful. If you have Firebug installed on Firefox, you can send messages using the Logger interface. You can use sever levels of notifications: Info, Debug, Warn and Error. There is also an AIR app that can be synced up to and gives a nicer interface. What I did not like about it though is having to use the swc. This is not too complicated, but if I'm handing over projects that are made for Flash CS3, the swc procedure is a bit cumbersome and can make it easy to forget about the swc. It's not a problem in cs4, because you can link to swc files, but this causes projects to be just a bit more difficult to switch between CS3 and CS4.

ThunderBolt works essentially like the trace feature, but I've found the FlashTracer on Firefox to slow down wight down the processor sometimes far too much, so Thunderbolt is a bit more helpful, as it allows to display objects and arrays easier.

Then I found out about De MonsterDebugger . This makes debugging what it should be. I always thought that the biggest shortcoming of FlashDevelop was the lack of a debugging tool, but with this debugger this is a issue of the past. De MonsterDebugger only requires one import, rather than the swc.
It supports the trace type of debugging, but more importantly it lets you browse through all the objects.
All you need to do is "debugger = new MonsterDebugger(this);" and the debugger console lets you browse through the available properties and methods.
An other handy feature is the ability to call any exposed method. The is great for doing simple tests where want to call a function without having to build an interface for it.

Check out GotoAndLearn's video about this debugging tool to get a good idea of the capabilities.