age spells it can pull. Before Potion of Illusion, it wasn't an issue, since it couldn't reliably generate infinite copies of itself (let alone 1-mana copies!). Blizzard recently changed Discover cards to disallow them from discovering themselves, and I would argue that the Pilgrim/Potion interaction is philosophically the same as (or at the least, VERY similar to) "discovering itself," leading to anti-fun "gameplay." I put "gameplay" in quotes, because as I mentioned before, it effectively prevents the other player from playing the game.
The only counters I can think of are Living Dragonbreath (to get around the Freeze portion and allow minion usage) and Flik Skyshiv. The Dragonbreath only works if you have it in hand, and even then it only addresses the Frost Nova aspect. Flik is a class card, which is nice for Rogue, but doesn't help any of the other classes.
You can waste the 1 mana pilgrims with Mindrender Illucia. You can kill them "over the top" with burn spells or charge minions if your board isnt' full.
If you shuffle bombs (or anything else) into their deck it re-orders the whole thing, and they can lose the combo by drawing Potion of Illusion
Otherwise, think of it like any other combo deck; once you draw the combo, you (probably) win. The difference here is that the combo stretches over many turns, and frustratingly grinds you down. I don't think it's a balance issue, but can see it as a fun issue. Then again, if you hate that you can just concede once the turtles start being played.
Remember that "played win-rate" isn't the only measure of a card's power. Pyroblast and Bloodlust have played WR in the 70s. Why? They aren't particularly powerful cards; what they are is finishers; You usually win when you play Pyroblast (or, say, Mind Blast when it was in standard) because playing that card IS your win-conditio.
Mage cards especially prime, box, and the hero. Priest garakrond as well.
I don't like the card that can swing turn completely and randomly. It feels waste of time to play against.
These are weird; Puzzle Box in particular gives you very much random gameplay; it can win for you, lose for you, or have very little effect. How much you like Puzzle Box is how much you like randomness.
Priest galakond is a different problem - infinite value. It makes an entire style of play difficult if not impossible. I don't know what, if anything, is the solution to that - or even if we need one.