What is the meaning of "often mistaken, never in doubt"? In what context is the phrase used?
It means a person who voices opinions with great confidence, even though he is often wrong. Someone who thinks very highly of his own intelligence or judgement but who is not really that smart.
I often say, "He's someone who never lets complete ignorance of a subject get in the way of having strong opinions about it."
It's often used in a military context, where senior officers often give authoritative-sounding answers without actually knowing anything about the topic. (In junior officers, this may be no bad thing; most training establishments teach 'better a bad decision than no decision'. But this is going off-topic.)
The phrase is a longer, slightly expanded way of describing someone who is cocksure.
feeling perfect assurance sometimes on inadequate grounds
See also the Dunning-Kruger effect.