Which word you would choose as a superlative of "wrong"?
The word that comes to my mind is irrational. An answer to an objective question may show solid reasoning but an incorrect conclusion or result due to incomplete information or some logical error. An answer that lacks reason or context, in that sense, might be deemed wrong in this more profound way.
Wrongest (as others here have suggested) is good; worst is also possible.
In fact, though it is slightly less specific about the nature of the problem, worst is actually the more idiomatic superlative in some situations. In my opinion, wrongest is usually best reserved for failures that involve a moral dimension.
Compare the following:
Webster's Third New International Dictionary gives wrongest as the superlative of wrong.
EDIT FOR OP WHO ACTUALLY WANTED MY OPINION ON SOMETHING
Yes, you knew it had to happen, that I would eventually be forced to step out from behind my adamantine wall of dictionary citations
and render an actual (pause for a gasp)
opinion or preference in which I had to abandon all pretense of objectivity
(and it is a pretense) and simply say what I would do in this case. Now, before you start ringing me up and asking for WWRD bracelets, I have to warn you that my opinions, although as close to fact as humans can possibly get, are still just that: opinions. And so, without further ado I shall state that the word I personally would use as the superlative form of wrong is, in fact, not a word but an image
but (heh hehe) since this is English Language & Usage and not Non-Verbal Semiotics 101, I will render the image in words. Soooo ... when someone is totally, completely, 100% wrong, the wrongest state of wrongness that can ever be achieved plus one, I would simply say
And I would leave the field triumphant, adored by the women, admired by the men, but keeping my hand on my car keys in case I needed to make a quick getaway in order to avoid bloodshed (mine).
Hey, you asked.