I'm running FC6 and gstreamer-totem play's .mov files fine for me. I followed the instructions here (
http://gstreamer.freedesktop.org/download/fedora5.html ) to add the gstreamer repositories and then did the following with root privileges...
yum install gstreamer-plugins-bad
yum install gstreamer-plugins-ugly
I would suppose the the codecs you need for .mov files mostly live in the gstreamer-plugins-ugly package but I'm definitely no expert on this stuff. But it does work fine for me...