Can I change the 17 inch wheels on my 2004 Mazda 6 to 15 inch wheels. ?

I was recently in Ohio and ran into someone who pulled the 17 inch rims off her car and put 15 inch rims on it. Since I am sick of paying $850 a set for 17 inch tires would this work on a Mazda 6 2004 hatchback - only thing I can see that would change is the clearance on the brake callipers might interfere. What else could happen here.