So. There were some serious security issues with Flash support in Quicktime. Apple released 7.3.1 to fix them. Unfortunately, they fixed them by disabling Flash support.
Let us step back for a moment. Quicktime plays Flash files? Yup, Quicktime will playback SWF files that are compatible with Flash version 5 or earlier. They can also be embedded as tracks within other quicktime files. Many content producers take advantage of this to add interactivity to Quicktime movies.
Needless to say, an update suddenly removing that capability has created some serious issues for a number of users. No warning, no downgrade path and no comments about workarounds. Sounds like classic Apple to me. Jerks.