How do cards like Zur's wierding and Glasses of urza affect cards like Hypnotic specter and Hymn to Tourach? I assume with Zur, you just turn the hand face down and shuffle it a little before letting the player pick a card at random, but for the Glasses, can a player cast Hymn, then tap Glasses in response to it to be able to see what card they are picking 'at random'?
Not that anyone plays Glasses, but I'm curious anyway

It's a random card. There is no way around this.
Best way to pick one is to just roll a die, assinging each card a number. Players should never let someone just pick a card out of their hand. Another option is to shuffle up the cards, put them in a pile, and have the opponent pick top 2nd, bottom, etc.
-Matt