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The discussions on this newsgroup helped me realize that another way of explaining the user interface in 1.4 may help people familiar with the 1.3 mechanism.
In 1.4 you add a domain to the whitelist by opening Firebug on a page in that domain. So for example if you open the URL http://getfirebug.com, then open Firebug, the domain getfirebug.com is added to the whitelist. If you subsequently open http://blog.getfirebug.com, Firebug will be opened because getfirebug.com is on the whitelist.
In 1.4 you add a domain to the blacklist by clicking [X] in the upper right corner of Firebug when Firebug is open on a page in that domain. Continuing the example above, while on http://blog.getfirebug.com, if you click the [X] button Firebug closes. When you go back to http://getfirebug.com, Firebug is still closed because getfirebug.com is on the blacklist.
A few details:
First the mechanism used for the tests is closer to the same-origin policy of Firefox than simple domain comparison. The case that will probably confuse people is http vs https: Firebug like Firefox considers http://getfirebug.com to be different than https://getfirebug.com.
Second, this description assumes you have 1.4b5 or later and that you leave the default option Activate Same Origin checked.