Firefox 3 was ignoring a cookie being set by an application running on localhost. The Safari 4 Beta on the same machine had no problems whatsoever.
Using Firebug’s console to set the cookie using the Javascript console, the problem was isolated to the domain of the cookie. Removing the domain specifier (‘localhost’) fixed the problem. Using the mDNS name of localhost also works. Why this is an issue for Firefox, and Firefox only, I don’t know.