Follow up from bug 611032 comment 61:
"- nsIConsoleService does not have a way to remove individual messages, or to clear all messages associated to a specific inner window ID. This means that the Web Console clear button only temporarily clears nsIScriptErrors. They show again after reopen.
This should be fixed inside the nsIConsoleService. The 250 messages limit is also hard coded..."
An alternate "solution" is to allow the Clear button to clear all of the messages, at once, from the nsIConsoleService. Meaning that any cached errors in the other tabs are lost. This is only a workaround - what we really need is a way to remove messages associated to the inner window ID we want.
We might want to base this bug fix on top of bug 692824.