if it says to make your opponent discard a condition,then you make your opponent discard one of HIS or YOURS or a 3rd guys' condition.
It has to say make your opponent discard his condition etc etc etc.If it doesnt specify whose card to discard u can do as u wish 
I am not sure if Shadow Player is allowed to discard other Shadow Player's cards if the text of the card doesn't specifically say so. If an opponent is chosen, then that opponent discards his cards. I'll mention
Sword of Dol Guldur. The text of the card says that Free Peoples player must discard a possession or a condition. That may lead someone to conclusion that Free Peoples player can discard shadow cards, but that is not the case. There is a clarification (not errata!) of the card that says that Free Peoples player must discard a Free Peoples possession or Free Peoples condition.
I mention this because it is declared as clarification, not errata. That means that the card text is not wrong, but someone might misinterpret it. That is why I think that when it says to choose an opponent who must discard a condition, then that opponent must discard his condition unless it says otherwise.
On most cards it does specify what can and cannot be discarded and who does the discarding so there is very little confusion.
example : http://lotrtcgwiki.com/pages/LOTR05080.html
usually arrow slits is used in order to discard a shadow condition or a machine but lets say that :
shadow player in shadow phase plays grima
maneuver phase starts and fellowship player discards arrow slits in order to discard a rohirrim javelin from eomer third marshal which already has firefoot and eomers' spear so grima cannot affect eomer's possessions.
I have used
Arrow Slits in that manner. It's such a nice card.
