In all seriousness, I don't think an age limit would make anything better. I understand it might eliminate candidates who could develop dementia or other mental health problems (or physical health problems for that matter) while in office, but a person's health and mental stability isn't always directly attributed to their age. I say that for the following reason...
I work in an environment which is heavily populated by the elderly. I work for people who are between the ages of 70-100 years old. And, you know what? The ones who are in their 90s are often the brightest bulbs on the Christmas tree (I know, lame, I'm sorry). Seriously though, there are people at my place of employment who are in their 70s and have zero mental capability; not enough to make decisions for themselves let alone other people. But, there are people who are 95 years old who are the most level-headed, down to earth, mentally capable, intelligent human beings I have ever met.
An idiot is an idiot. And, if a person is an idiot when they're 80, chances are they were an idiot when they were 40.