@MeanMrMustard:
mentally would have to consist of something more than just "I don't agree with him"... it would be serious mental impairment that made it impossible for him to function. What that looks like is different for every individual. It could be memory issues, incapacitating depression or anxiety, delusions or hallucinations....many people function well with any of these issues - so the key is incapacitating - something so severe he was unable to make rational decisions or carry out his duties.
physically it would be something like a coma. He could serve as President even if he was a quadriplegic or on bed rest if he was otherwise well.
conflicts of interest I was thinking if the President started working against the interests of the US in favor of a foreign government, or was otherwise actively attempting to dismantle or thwart the government.
The 25th Amendment was adopted after Nixon. Gerald Ford had to replace Spiro Agnew as VP, and then Nixon as President because they were both crooks. The wording is "President is unable to discharge the powers and duties of his office," - that is open to interpretation kind of like "high crimes and misdemeanors" So, I'm not sure the intention is that it is only used when the President is incapacitated mentally or physically.