The failure of psychohistory is not strange in itself. The idea of psychohistory is that large numbers of people are capable of statistical treatment - even important people are unable to overcome the statistical effects of large numbers of common people. Mutant like Mule, however, breaks down the assumptions.I find it strange that something as scientific as mutation cannot be accounted for by psychohistory, meaning that the mules function in the story makes less sense the more I think about it.
Asimov kinda needed something to throw a wrench in the works though.
What´s odd, however, is what Mule does.
If it´s acceptable for him to leave his army for a year and hide under a false identity... why did he bother with army in the first place?
With the powers he discovered by age 22, the quickest way to wealth, power and influence would have been simply to get a passage to Terminus, get a job as a clown in Indbur´s court and take over Foundation from inside.