The cards I have a problem with are actually Mindvision and Throughtsteal.
First, they can't be played around. A Priest can copy an amazing card you drew into on turn one, after a mulligan. Thoughtsteal just copies from your deck, so there's nothing you can do there either.
Second, they allow the Priest to have access to cards they shouldn't otherwise have. It's pretty rough getting around things like the two copies of Ragnaros the Priest happened to copy (as happened to me many games ago), or the Polymorph and Flamestrike I got hit with last game.
Most importantly, though, it gives the Priest MASSIVE card advantage, which is devastatingly powerful for a control deck. In my experience, Priests tend to run the game down to the wire, where both opponents are left with next to no cards in their decks. In this scenario, Two copies each of Mindvision and Thoughtsteal give the Priest six extra cards in hand, without depleting their deck at all.
By comparison, the closest card to Thoughtsteal is the Mage's Arcane Intellect. Pay three, draw two. These two cards come from the Mage's own deck, though, thus depleting him closer to fatigue damage late game. This is something most Mages have to deal with if they're playing control (or against a control player): they're going to draw a lot, but at the expense of running out of cards late game.
The closest non-Priest card for the same cost is the Hunter's Flare, which is situationally nice, but in most games amounts to nothing more than a simple pay one, draw one. Again, though, this comes from the player's own deck.
It could certainly be argued that Priest can potentially draw into cards that do no good for them (e.g. "give your weapon +X/+X", etc.), but more often than not, they can put the cards to some kind of use. Even crappy beasts can be used as fodder, and sometimes they hit pure gold with the cards they luck into.
I am not claiming that these cards need to be removed from the game. I will never advocate such drastic changes to a game. I do, however, think the benefit the cards give them is insanely underrated and incredibly useful, and think the cost for both cards needs to be tweaked.