Flash Logging API
No correct solution
I've been using Thunderbolt. It allows you to see your log results in Firebug.
I developed and manage Loggee!, a Flash/Flex Logging Tool: http://davidbuhler.org/loggee-flex-logging-tool/
You must see http://sourceforge.net/projects/log4flash/
with no more.... bye bye
I would recommend Arthropod if you are looking for a development tool (this wasn't very clear in your question), if it's to log your client's behavior, I'm not aware of any tool sorry.
I always end up writing my own logging solutions. They generally are very simple compared to the rest of the project, and by writing my own I can tailor it exactly to what I need. Whereas using a pre-built one, always seems like either it is too over-engineered and complex to use, or it's too simple and lacking a couple features I need.
Try to use Log5F logging utility for ActionScript 3.0