gun, those too, are some of the symptoms I had, as well as other people have, with this MSP stock radio. It's simple, the unit is shorting out and all kinds of crazy s*** is happening.
Imagine the metal data connections touching between the detachable face and the unit behind it, getting moved back and forth, becoming mis-aligned, and god-forbid, overlap, as you press on the face and the buttons over and over trying to figure out what's wrong with the radio. The face is bound to move around a little when you press on it, especially if the side-spring-plates are in a weakened or inwardly-bent state and need to be stretched out again so the face can be held in place tighter and better. Usually, I believe, only the left-side spring needs to be stretched out a little and rigidified so the metal data connections line-up exactly and the overlapping (shorting) stops.
So, if you are having any symptoms of your radio doing crazy eclectic s*** you could've never imagined, it's probably just shorting itself out, in which case you're lucky there's such an easy way to fix it. Otherwise, maybe you'll have to visit your always-lovely local Mazda service department.
Good luck. (boom07)