The Flash plug-in stores its temporary files in /private » var » tmp » folders.501 » TemporaryItems, in files named FlashTmp0, FlashTmp1, and so on.
So if you want to do a quick save without looking at Safari's Activity window, press Command-Shift-G in the Finder (or use the Go » Go to Folder menu item), enter /tmp, and dive down the specified folder hierarchy. You can then move the FlashTmp0 file to the Desktop, add the .flv extension, and watch it with VideoLanClient, MPlayer OSX, or QuickTime with the Perian.component installed. I tested this with Safari and Firefox 3 beta.
Mac OS X Hints