I agree that Paul's behavior could be erratic but I found something interesting on Wikipedia:
The popular view of Paul I has long been that he was mad, had a mistress, and accepted the office of Grand Master of the Order of St John, which furthered his delusions. These eccentricities and his unpredictability in other areas naturally led, this view goes, to his assassination. This portrait of Paul was promoted by his assassins and their supporters, and has become accepted wisdom mainly by repetition.
Comparatively recent research has reconsidered and rehabilitated the character of Paul I. In the 1970s, two academic panels provided the assessments of new research into Paul I: one at Montreal in 1973 and the other at St. Louis in 1976. Some of the findings were presented in a book edited by Hugh Ragsdale in 1979: Paul I: A reassessment of His Life and Reign, University Center for International Studies, University of Pittsburgh, 1979. The reappraisal of Paul I has demonstrated his character as someone of high morals, who followed his conscience.
Paul suffered a lonely and strict upbringing, and whilst he was eccentric and neurotic, he was not mentally unbalanced. Though an analysis of his biography reveals an obsessive-compulsive personality, he had "characteristics fairly common in the population at large". Where Paul differed, was that by 1796 he had to manage the whole of the Russian Empire.
Though I don't agree that he wasn't unfaithful, I do agree that he wasn't mentally unbalanced. Though surely open for debate, it is nice to read that people are reconsidering their position on this unfortunate man.