While it should not be necessary, apparently some have found it worth the effort to first remove their current Flash version (Computer/Library/Internet Plug-Ins/Flash Player.plugin).
And of course, ensure you DL the applicable PPC or Intel version.
On both my PPC and Intel machines, a subsequent Permission Repair found numerous items to fix. AFAIK, this is typical and is no cause for alarm, just something to ensure is done.
A quick test of the new Flash indicated no problems. Still, having a verified backup can’t hurt.