1. While you search for your card, the game carries on and things continue to happen in the background and you lose precious time away from micro-managing your cards.
2. The interface for searching your card is displayed like packs in the Card Store. You'll have to scroll through your deck until you find the card you want, all the while with the pressure of the game continuing in the background. You can't cancel and will be stuck there until you finish selecting.
The above 2 factors make card tutoring less useful in my opinion in this game. One suggestion to fix this will be to display your entire deck on screen.
iTunes App Store link: