I am planning to visit Istanbul and the Blue Mosque. I would visit the mosque before prayer time but I am interested in observing the prayer and therefore I would like to stay a bit for the beginning. I guess my question is, as a Non-Muslim, would it be considered rude to observe the prayer? Also, would it be rude if I left during the prayer (midway through let's say)? Obviously I would be quiet, respectful and near the sides so as not to disturb the people that are praying.

Tu ne serais pas permit a l'interieure.

You are expected to show some respect in houses of worship, whether these are churches, mosques or temples. And that means not disturbing any prayer time.

As a non-Muslim you will not be allowed into the Blue Mosque during prayer times.

As long as you are clean you can participate in the prayer in which you will be submitting yourself to your creator. But since you are a non Muslim you don't know the rules regarding behavior inside a mosque it is advisable you remain in prayer till its over. After all Muslim prayer lasts only about ten minutes. By the way when you pray to God you become a Muslim, the meaning of that word is submission to Allah. Great enjoy your spiritual journey towards your creator who is most gracious and most merciful.

I would check ahead and ask permission of the mullahs who run the mosque. The way you asked here seems perfectly polite.

They are so used to people going in and out of it, and it is HUGE, that I doubt they'll even notice you.

paint it red dude