I do see what it literally means (“I can to/for myself to be wrong”), but I would have thought it would instead have been “potrei avuto essere sbagliato.” Is this a common usage – turning essere into essentially a reflexive verb?
I think the point mentioned by @David755502 is correct.
I don’t think the mi really belongs to essere - or as you put it in your original post, turning essere into a reflexive verb.
I believe that the mi is from sbagliarsi, where that is the reflexive verb.
So the sentence would then be made up of - Posso esser(e) + mi sbagliato
Then the mi throws itself into the loving arms of essere who willingly sacrifices an “e” in order to make the sound more beautiful.
If the sentence were instead to have used the intransitive form of sbagliare, then it would likely have been translated as Posso aver sbagliato (N.B. the original sentence needs essere to act as the auxiliary for the perfect tense of a reflexive verb).
I’m not sure about the reason for the choice of tense for potere here, and whether the present indicative has some significance instead of using the conditional (for example whether that implies a greater degree of certainty).