> Weren't these issues with 64 bit OS only due to the protected mode now included with Flash?
No, it was Low Integrity, on both 32 & 64 OS's.
> I don't think protected mode runs on XP.
Most likely right on that, in particular on x86.
But again, it would be Low Integrity, & Adobe did not add that feature to Flash for XP systems.
> Does it run under vista/win7 32 bit?
Yes, Low Integrity would run on Vista & up OS's.
Yes, you're right, they do call it "Protected Mode". (I was thinking more of Windows "Protected Mode.")
Inside Flash Player Protected Mode for Firefox