A lengthy report by the Department of Justice on President Biden’s handling of classified documents contained some astonishing assessments of his well-being and mental health.

Mr. Biden, 81, was an “elderly man with a poor memory” and “diminished faculties” who “did not remember when he was vice president,” the special counsel Robert K. Hur said.

In conversations recorded in 2017, Mr. Biden was “often painfully slow” and “struggling to remember events and straining at times to read and relay his own notebook entries.” So impaired was Mr. Biden that a jury was unlikely to convict him, Mr. Hur said.

Republicans were quick to pounce, some calling the president unfit for office and demanding his removal.

But while the report disparaged Mr. Biden’s mental health, medical experts on Friday noted that its judgments were not based on science and that its methods bore no resemblance to those that doctors use to assess possible cognitive impairment.

In its simplest form, the issue is one that doctors and family members have been dealing with for decades: How do you know when an episode of confusion or a memory lapse is part of a serious decline?