When viewing hand history at Full Contact Poker does it show mucked hands at showdown. ie - If a player bets on the river and is called and shows the winning hand and the other player mucks....does it show the mucked hand when viewing the hand history?

nope

The hand replay feature only shows your cards and the cards that were shown down at the table.
The e-mailed hand history feature is one of the things that is in the process of being fixed and I believe it should show all hands that were live at showdown.

A new hand history system is being developed as well but that will take a bit longer.

I'm probably in the minority, but I actually like it the way it is now, where your opponents only get to see your hand if it is actually shown at the table. It's more like "real" poker as is.

(Maybe if there was an option to request full hand histories for certain hands, for the sake of providing a means to look for evidence of suspected collusion this would probably be good - something equivalent to the option you have at a casino to view a mucked hand that went to showdown if you suspect collusion.)

Although, at the same time, I am really hoping that the note-taking feature gets fixed soon.