Why wouldn't you be able to?
The discard pile (both of them) are public information. Meaning that both players can look at them without anybody questioning it. Same goes with looking at which of your opponent's Pokemon are Rare Candied, the attacks of them, and everything else on it (just be sure not to do that every turn because people may call you for stalling). Players prizes aren't for anybody to see (except for a judge and when a player uses Azelf Time Walk). The hand of each player is only for the player themselves. And the deck is private to both players unless they are allowed to go into it by some form of attack, power, or trainer/ supporter.
Hope that clears things up a bit.