If I switch to a different network while Firefox is open, Firefox won't check for a new WPAD server and PAC file. Since the old PAC file isn't likely to work on the new network, everything breaks (I get errors that Firefox is configured to use a proxy server that can't be found). Going to Preferences, changing the proxy setting to Direct, then changing it back to Automatic solves the problem. It's my understanding that whenever a network connection changes (e.g. an ethernet cable is unplugged or plugged in, or you connect/disconnect to/from an AirPort network) the OS sends a signal to all applications informing them that there's been a change. Firefox needs to respond to this by looking for a WPAD server on the new network. Sorry, I don't know the technical details. And, I don't know if this is a platform-specific bug or not.
Does going offline and online work?
No, going offline (I'm assuming you mean the "Work Offline" option) and back online does not fix it.
Yeah, Mac OS X would need platform specific code for this... I think this is related to the feature development in offline-online, so I'm "improving" the summary.
NOTE: I was reading the PAC code last week, and offline-online does appear to call PAC when you go online. This may not have been in place in 2006... So anyone else affected, give that a try. There are a couple other related-sounding bug reports that say this is working now.