Will different tire size on the front and back cause transmission/driveshaft problems?
Depends really.
If it's only FWD, and assuming you keep stock size on the front, probably no drivetrain damage but you could affect handling, braking and overall safety. And if something does go wrong, warranty will be void.
But if AWD...
Depends on how much difference in the diameter of the tires.
A very very very small difference might not cause immediate problems although it will cause your drivetrain to wear out more quickly. You may not get any dash warnings but it will still cause slow wear, maybe damage will show up a year later, a few years later or several years later... Who knows?
You will also be voiding any warranty you have.
However most of the time...
*Assuming that the mazda has warnings like other vehicles...
most often there will be dash warnings lights that the "transmission is overheating and to stop the vehicle immediately."
This usually occurs after driving a few miles and when you get that warning light , if you continue to drive, you will be burning up the tranny and causing damage to the tranny & pumpkin. Again, warranty will be void. And you will also have handling, braking and safety problems.
If you really want to run bigger tires in the back, take it a mechanic and get his opinion on what you may be able to safely run.
