Even if the medical had uncovered a serious mental health issue, the public would not know about it. The president is granted the same rights to health privacy as everyone else. This means that he is allowed to decide what details about his health are released to the public.
In his assessment, medical professionals could have diagnosed him with Alzheimer's or dementia, but the public would have no right to that information. In fact, it is almost certain that any mental illness would not be disclosed out of national security concerns.