Can an action be mirrored? Is there a way to mirror actions that were keyed for one side to be mirrored to the other side? 



I tried to add another x-flipped action as the button (green 1) does for the current pose. 
This button is only available in the pose editor. 

Then I tried to copy and paste key-frame by frame (from green 2 to red 3) but it seems that we can't have two different views of the action editor. (When the selected action is changed in one action editor the other one copies the change and displays the same action)

How can an action be x-flipped mirrored into another action?
To extend Leon Cheung's answer (my reputation isn't high enough to comment yet), you can achieve the same thing by selecting ALL of the keyframes from the Action Editor (press A) and pressing CtrlC, and then pressing CtrlShiftV to paste the flipped animation somewhere else. This works for the WHOLE animation, and can save more time than doing it manually (and is a whole lot less error prone).