My guess is that his good and evil sides would split off from each other entirely, and you'd have two people, both Mask-enhanced. One would be a sort of super-lawyer, acting not only as judge and jury (but NOT executioner, 'cause this is the good side), but catching them and bringing them to trial himself - the other would be a horrible, twisted, demonic gangster-figure who'd make the villain in the 'Mask' movie look like a fuzzy bunny. Batman would have to catch BOTH of them and bring them back together, since he could only remove the Mask once the two sides were reunited again.