Evan Osnos of The New Yorker writes about the possibility of removing Trump from office. One avenue for removal is Section 4 of the 25th Amendment. It allows Congress, or the VP and Cabinet officers, to declare the president unfit to discharge his duties. After such a declaration, the VP immediately becomes Acting President. The president can challenge the declaration, at which time Congress has three weeks to decide on permanent removal. A 2/3 majority vote is required to remove the president under this provision.
This isn't likely to happen, both for political reasons and because the question of fitness isn't cut and dried. Furthermore, the term "mental disorder" shouldn't be equated with lack of fitness to carry out one's duties.
As Osnos points out in his article, a study conducted at Duke University in 2006 estimated that 1/2 of all presidents have suffered a "mental illness" at some time during their lives. If the standard for declaring mental illness is a DSM diagnosis, then that figure doesn't seem impossible.
But the implications of DSM diagnoses vary greatly. Many people who meet the criteria for a DSM diagnosis are capable of carrying out their job duties. It doesn't seem to me that we're in a situation that incapacity to carry out duties is likely to be declared. I imagine that, had the 25th Amendment been in place, Garfield and, later, Wilson, might have been removed from office under such a provision.
Which psychiatric conditions might constitute a basis for removal under the 25th Amendment? Probably not any personality disorder. Either a psychosis (hallucinations, delusions, thought disorder, frank mania), an immobilizing depression, or an organic condition such as a dementia or some other neurocognitive impairment.
There has been talk of the latter. For example, this person (who seems to be a neuroscientist but not a clinician), some in the media and a number of psychiatrists on line, have been quite insistent Trump shows signs of a dementia. I also know through a friend that someone who was until recently in Trump's inner circle is saying that he's suffering from a dementia, but he's a politician, not a clinician. I'm not going to out him, but I do wish he'd go public with his opinion.
Anyway, unless something changes, I doubt we'll see a removal based on the the 25th Amendment, and I wouldn't really want to see that unless it was absolutely merited by functional impairments that would qualify as incompetence in civil or criminal proceedings. That leaves lots of room for a president to be quite the mad man without being removed from office, but mad men can be capable of carrying out their duties, even if we'd be horrified by how those duties are discharged.
I'd prefer, instead, that anyone be free to give their opinion on the mental functioning of public figures, and let the public pass judgment based on its assessment of such input. I still expect to say more on this subject, but for now I wanted to clarify that I'm not proposing that Trump be removed from office based on public assessments of his personality.