Advice on windows going down automatically when shutting the door randomly?

I'm looking at a 2008 GT and as i took it for a test drive and parked the car the front windows went down half way after i closed and locked the car. The next time they went down all the way and no i didn't hit the unlock and hold it. Also the mazda remote starter would turn the car on and then off again every minute as in startup,shutdown,startup....

Is there something i should tell the dealer to start looking?
 
Find another one. That is what I would do.
You never know how long it might take to debug such a problem.
 
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