If Mozilla is open and you activate it through the dock, it doesn't open a new window. Metaclarity's freeware Mozilla AppleScripts remedy this problem.
Both scripts are identical (and quite easy to understand; take a look at them with ScriptEditor if you're new to AppleScript and want to see how they work), but the first is saved as an application so it can be put in the dock. Clicking the dock icon activates Mozilla and opens a new window. The second is saved as a Script for the AppleScript menu. Drop it in the ~/Library/Scripts folder on you drive and you can activate Mozilla and open a new window from wirthin any application.
[Editor's note: The script worked as expected when I tested it. In browsing MetaClarity's site, they also have free scripts for various tasks in BBEdit, the Finder, and iTunes.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20020426081639225