the airconditioner and the rearview mirror

What is your question?

In the last couple of weeks, when I start the car, the airconditioner fan doesn't always come on. It sometimes comes on after driving for 5 or 10 minutes. Another trouble that started about a month ago is that occasionally the rearview mirror will darken as if there were headlites behind me and this is in broad daylite. Most of the time if I give the mirror a good tap with my hand it clears up the problem and then it occurs again when I get into the car at a latter time in the day or a day or two later. HELP!