The office to which Trump aspires is the most powerful in the world. It requires an enormous amount of diplomacy and rational behaviour on the world stage. It is not a position suitable for a petulant, argumentative, immature megalomaniac. He only has to open his mouth to demonstrate how unfit he is for the office.
Yes, Donald Trump, based on his statements that promote violence, racism and gender bias, is mentally unfit to be president. Trump has voiced vulgar, egotistical and discriminatory comments that display his blunt and politically incorrect views. The U.S. needs a president who can control his temper, negotiate with foreign allies and foster the growth of the nation without spurring hatred.
It's impossible to look at Trump's entire life up to this point, not just his campaign, and come to the conclusion that he is a mentally stable and balanced individual. Clinton said that he could be baited with a tweet, and he went and proved her right immediately. People shouldn't be disqualified from many jobs due to mental issues, but President of the United States is one of them.
Yes, Donald Trump is mentally unfit to be president, though his statements are not proof he is mentally ill. They are proof that his mentality is one of hate, fear-mongering, and inexperience. No one with these mental elements should be allowed to run in the election, let alone become president.
He is not mentally unfit, he just doesn't have the same way of approaching issues that traditional politicians do. Politicians tend to all go to the same school of manners. They speak a certain way, try not to ruffle feathers, and try to appear efficient. Trump might sound mentally off to people who have never encountered unpolished speakers before.