If you're having trouble with Flash movies and the latest version of QuickTime (7.1.3), it's probably due to a new setting in the QuickTime System Preferences panel. In my case, I couldn't see any Flash previews in the Finder, as one example of the broken behavior. As noted on Apple's discussions site, in this thread about .swf files on iWeb, there's a new Flash-specific setting on the Advanced tab: Enable Flash, which is not enabled by default.
To change it, simply check the box. As noted under that setting, you'll have to relaunch your applications for the settings to take effect. On my machine, after enabling Flash and restarting the Finder, I was again able to see Flash movie previews again.
It seems that many people will not automatically think to check their preferences -- but do so before going elsewhere screaming that Apple broke their favorite function with this latest update.
Mac OS X Hints
http://hints.macworld.com/article.php?story=2006091307524042