Chapter 23's first issue is a familiar one, the question of whether we should let others see our good works. I'm standing by my answer in chapter 5, namely that it's not so much whether you're seen, but what your intentions are.
Next, it asks whether it is OK to call anyone "father". Frankly, this verse has always confused me, since Jesus doesn't seem to make exception for our earthly fathers, and I've actually met people who feel this is the right interpretation, although it seems absurd to me. I think that the best interpretation (my opinion) is that this verse and the following are saying that people of religious authority should not take fancy titles for themselves, and it has little to nothing to do with parenthood or slavery.
Then Jesus lets loose with some harsh language for his detractors (again I stand on my answer in chapter 5 concerning the term "fool") which I'd say you need to decide for yourself whether they deserve it. After all, in verse 31, when Jesus calls them "the children of them which killed the prophets" he's technically telling the truth. Now when he specifically mentions "Zacharias son of Barachias" there does seem to be a problem there, as the name "Barachias" doesn't seem to appear elsewhere in the Bible, and the easily-identified Zacharias does seem to be the son of Jehoiada. I don't have any easy solutions for this one, the only things coming to mind are that "Barachias" may have been a grandfather or great-grandfather, or alternately (but more of a stretch) "son of Barachias" may have been some sort of title, as "Barachias" means "blessing of Jehovah". I really don't know, although it might be worth noting for better or worse that there was another "Zechariah the son of Jeberechiah" mentioned in Isaiah 8. (That could be source of the solution OR the problem, really.)