On most AWD/4WD vehicles it's absolutely critical that all four tires be exactly the same diameter. Width doesn't really matter that much (although width can change the diameter, since a 70-profile is different in diameter than a 60-profile), but diameter is critical because if it varies, the number of turns per mile is different for each axle. That will destroy transfer cases.
The same is true for RWD vehicles on the rear axle - if the left and right tires are turning a different number of revs per mile, you'll damage the differential.
That said, you need to get a detailed, specific explanation of the problem from the dealer. If the vehicle was driven with mismatched tires, it's not their fault. It may be something you need to talk about with whoever sold you and installed the tires. They should know the importance of this. But if they advised against what you bought...you may not have any options.
I agree - I'd like to hear what sizes are on the vehicle, and which corners they're on.