Things I liked
The style of detection was different from what I'm used to with Agatha Christie. Her detectives Disapprove of murder with a capital D - as of course they should. But what I liked about Father Brown was how it dealt with the human side of each case. It wasn't labeled from the beginning that a man is a murderer, he is evil, he was born wrong and must be condemned. G. K. Chesterton showed how a man is a man first, who then commits a murder due to his baser instincts. There were also the cases where the murderer had no pity from the reader, but nevertheless, we always saw his human side. Because it's ludicrous to suppose that lines can be drawn. Everyone has the capacity to commit a crime. Father Brown understood that and being a priest judged accordingly.
I also enjoyed Father Brown's beliefs of the supernatural; How he didn't believe in it despite being a priest. It was supposed by many characters that he would, but his clear-sightedness always saw past all that to the reality.
Things I didn't like
Most of the time in the stories I was disappointed that G. K. Chesterton ended up killing off the murderer with suicide. It was as if he didn't want to deal with the character after he had committed a crime. As I said before, the book dealt nicely with the development of the crime, but it was tidied up so as to not deal with the after effects. It wasn't done in every story, but often enough to annoy me.
Father Brown was a very astute detective, but many times, even when he was introduced before the crime or murder had been committed, he failed to solve it in time. I might be asking for the impossible here (although that is precisely what Hercule Poirot does in the short story Wasps' Nest), but if he was able to read humans so well, he might have made an effort to dispel the tension which naturally led to the murders.