A player should not be allowed to see his Discard pile
According to Dominion rules:
"A player is allowed to count how many cards are left in his Deck, but not in his Discard pile. A player may not look through his Deck and his Discard pile. A player may look through the Trash pile, and players may count the number of cards left in any pile in the Supply"
("Additional rules", page 4)
So, it seems there is no need in "Show Discard" button as it contradicts to the rules. Also, we should not display number of cards left in discard pile.