The X3 needs new rear tires. Standard size is 235/55/17. I have two 225/45/17 just sitting in my garage. What would the problem be if I slapped these on? Other than they would look odd in comparison with the other two?

The speed would read much higher than it actually is. I don't know if the ABS would freak out either, but it's a possibility.

That and it would look stupid.

The X3 needs new rear tires. Standard size is 235/55/17. I have two 225/45/17 just sitting in my garage. What would the problem be if I slapped these on? Other than they would look odd in comparison with the other two?
The height of the stock tire is 27.2" while the height of your extra tires are only 25". According to the page below, it is 8.1% too fast, meaning that when the speedo reads 60mph, you'll only be going 55mph.

http://www.miata.net/garage/tirecalc.html

that, and it's AWD so that would accelerate the wear of the diffs.

Big no-no to switch up tire size on any 4WD. Also agreee that ABS and any traction controle will get confused.

Don't do it. Breaks lots of stuff.