Can the player skin for a Flash video sit in a different directory or level on
the server from the .swf and .flv files? I can't seem to make this work, have
checked file permissions and everything else I can think of. I have tried
putting in both relative and absolute paths to the skin file in the fla file
but still no luck. I really don't want to have to store 100 copies of the skin
file when I have video content separated into folders, but.....?

Yes it can be done. On the component inspector or where you pick the skin
select "Custom URL". Put the relative path to your skin file in there. If I
remember correctly (unlikely) the url is relative to the html file calling the
swf, not the swf location or the flv file location.