"The firing pin doesn't seem to have any tension holding it to the rear... Should there be a firing pin spring holding the firing pin to the rear?"
I don't think so, but you might want to ask here:
http://leverguns.sixgunner.com/forum.asp?FORUM_ID=2
"The last round ended up with a light primer strike, and did not fire."
The light strike could be caused by crud around the firing pin, a weak main spring, a burr on the firing pin, etc.
If it keeps happening (and you're unable to correct it yourself) this guy is great at working on the Rossi:
http://www.stevesgunz.com/