I posted this issue first to http://scientificlinuxforum.org/index.php?act=ST&f=16&t=1803. On the forum, tux99 suggested I report this on the devel mail list.
After upgrading from SL 6.0 to SL 6.2, system startup appears to hang when it tries to start run level 5. Parallels is still able to cleanly shut down the guest OS and booting into single user works as expected.
After booting into single users, in the /var/log/Xorg.0.log file, I see that the Parallels video driver "prlvideo" cannot load because it includes an undefined symbol: "miEmptyData". The Parallels mouse driver cannot load because of the undefined symbol: "dixScreenOrigins".
Then Xorg aborts because it cannot find any screens.
CentOS release 6.3 with the same version of the kernel (2.6.32-279.el6.i686 #1) and the same version of Xorg-server (1.10.6.1.el6.centos) as SL 6.2 runs normally under Parallels.
This seems like a bug in SL to me.