Though I've been reading a lot of the blog entries that came out, I would have to disagree that it's easy to find these ironies. Maybe this work is rife with them, but I had a hard enough finding one example much less the "dozens" that I know others acclaim to have done.
That being said, two paragraphs that extend from the bottom of page 102 onto page 103 were the ironies that I found. In this passage, Hank is basking in the success and advancement of his set up schools and 19th century towns. He notes something about despotism which is where I believe the irony is. Hank says how an earthly despotism is the worst form of government because even if the "perfectest individual" had control, this individual is perishable and will pass on his kingdom to someone imperfect. Regardless of that statement, Hank goes on to say how much work he has done with the resources of a kingdom at his hands. In this sense, in order for Hank to be able to recognize himself as a despot and not one of the earthly despot governments, he would have to be considering that he is of the "despotism of heaven." In this sense, he is associating himself with G-d and the only other people at the time that had kingdoms' resources and a “despotism of heaven" (or so they believed) was the Roman Catholic Church.
Hank has said over and over again how many evils the Roman Catholic Church has committed. Yet, Hank strives to become them, to create his own sect of churches (where you can be any sort of Christian you like... except not Roman Catholic) and schools and influence how the people of 6th century Britain think. At the end of the second paragraph he recounts how exponentially his human assets have grown, “…where I had a dozen trained men then, I had a thousand now; where I had one brilliant expert then, I have fifty now.” He talks about having his own military and naval academy and all of it he keeps especially hidden from the Roman Catholic Church. It is because he wants to replace the Roman Catholic Church, not just overthrow them. He assumes that he has more right to plan out society than the Catholic Church because he is from the future. He speaks highly of democracy but really it is only he that can decide how things are done because only HE is from the 19th century. Therefore, while Hank strives against the Catholic Church, he is also striving to become the Catholic Church, merely with a different name.
Maybe Twain doesn’t know if he is making this irony or not, but replacing science with faith as a despot makes no difference; it’s still a despot. The fact that the protagonist, the guy everyone routes for, is looking to become a despot and keeps giving excuses on why it would be better for him to “rule,” it’s all just things that the Roman Catholic Church has been doing for centuries beforehand.