What are the weaknesses of the Miracle Rogue deck?

1) Rush decks, as mentioned in some of the comments, can flat out kill a miracle rogue deck before it can set up its combo. Rogues don't have particularly good mass removal.

2) Lots of taunt spread out across multiple creatures. Some folks recommend divine shields as well (e.g. Sunwalker). But you don't want to blow all your mana on a single card or the rogue is just going to sap it. Look for 3-5 health minions, to avoid Backstab one-shots, and to make it card intensive for him to clear your board.

3) Well-timed secrets when you think his combo is coming soon, can stall him or cause him difficulty choosing how to navigate past them. Ice Block, Vaporize, etc... Even Counterspell can break up his combo. He won't want to attempt it until all your secrets are cleared.

Acidic swamp ooze might be useful to nuke some of his removal if he's stacking Deadly Poison on the Assassin's Blade. Depends on your deck.

Edit (update):

4) Random or Area targeted spells that can take out the Auctioneer while he's Concealed are useful against this deck.

Loatheb is a useful card to have in almost any deck. Its Battlecry will delay the Miracle combo or slow down the auctioneer card draw for one turn while putting a strong body on the board. Nerub'ar Weblord doesn't fit in every deck, but is generally useful against zoo and will limit the Miracle combo by making Leeroy more expensive to cast.

I agree with spudone about including an Acidic Swamp Ooze.

Not only Loatheb, Nerub'ar Weblord is pretty good against miracle rogue, it's cheap, it's better than a cheap taunt because 6 cost Leeroy(or 5 cost arcane golem) can break most of miracle rogue combo(And miracle rogue also uses lots of other cards with battlecry). Besides that, this card wont be a dead draw in most of cases, since it's also extremely good against zoo, which is really popular at the moment.