Whoops, forgot to update.
Well, my power window "problem" isn't actually a problem as it turns out. It actually IS something Mazda installed in ALL of its newer cars.
My visit to the car dealer took awhile (getting a back window replaced), but I told them about the other "problem," and the guy in the service bay snickered at me when I explained what was happening. When he told me about this "surprise" feature Mazda put in, I wanted to
him.
I finally found something last night in the owner's manual that very briefly discusses how if you press the unlock button once, then hold it down again, both front windows drop immediately.
I have never heard of such a feature before, and honestly, I don't like it all that much.
Also, according to a message board posting I discovered, that it can be reprogrammed to not do that. If the car had a moon/sunroof, the remote would allow it to open too.