Does being in the military make you qualified to be President? Yes, if you accomplish something, like your job. Being a POW for a long period of time is more of an indicator of mental trauma than it is of leadership. Ask the guys at Gitmo.
Being a politician should automatically disqualify you from being president. It should be an honor to serve your country, not a requirement that your country serve and obey you. It's funny (peculiar, not haha) how that's changed in the last forty years. There's more to being President than getting elected, just like there's more to being a parent than the ability to reproduce.
Running for one office while not having completed a third of the office you are currently holding tends to show that you either have a problem keeping the same job for any length of time or that you are in it for the power, fame and fortune. Fortune used not be part of the equation, but that has certainly changed since the invention of the speechwriter. And cronyism.