Arthur Dimmesdale is just as guilty as many other Puritans for leading a life where he could pick and choose which mandates to follow, and which not to follow.
The problem is that a man as well-educated, experienced, and placed in a position of power, should know that he is doubly responsible to lead a life of righteous behavior if he is meant to guide others to do the same thing.
In that respect, he is essentially hypocritical, and a liar. Even he admits to as much. This is why he feels that he should take the lead and play God upon himself by applying his own punishment.
Else, I should long ago have thrown off these garments of mock holiness, and have shown myself to mankind as they will see me at the judgment-seat. Happy are you, Hester, that wear the scarlet letter openly upon your bosom! Mine burns in secret!
This statement by Dimmesdale is a travesty of the truth. If he were a good man he would have openly accepted what he did and accepted his fate.
Another huge problem with Dimmesdale's reputation of being a "young divine" comes from his complete disconnect from Pearl. Yes, he does admit at the very end (on the day of his death, no less) that he is Pearl's father and is graciously forgiven by Pearl. But from the get-go we see that Dimmesdale has no interest to connect with Pearl, not even in secret. During the secret meetings in the forest, Hester basically begs Dimmesdale to "like" Pearl, assuring him that, once he gets to know her, he will love her like a father would. Sure, fathers of that time period were not meant to be warm-fuzzy by any means, but Dimmesdale does not even attempt to appear agreeable toward his own flesh and blood. He is even worried that people may find a resemblance to him!
,[..] this dear child, tripping about always at thy side, hath caused me many an alarm? Methought—O Hester, what a thought is that, and how terrible to dread it!—that my own features were partly repeated in her face, and so strikingly that the world might see them! But she is mostly thine!
Basically Dimmesdale shuns any responsibility toward Pearl. She is "mostly Hester's". Could this be, in a very primitive way, a dig at Hester's inability to prevent a pregnancy in the first place?
Finally, Dimmesdale is obviously guilty of lust. This incident with Hester may not have been the only time that "nature" has called his name. In chapter 20, Dimmesdale literally loses his mind after leaving the forest and does all sorts of insane things. One of them was to go to one of the most virginal women in his flock and say salacious things to her.
Such was his sense of power over this virgin soul, trusting him as she did, that the minister felt potent to blight all the field of innocence with but one wicked look, and develop all its opposite with but a word
Despite his mental turmoil, Dimmesdale should have known better than to commit these very serious acts.