We watched the entire first series, with the children, and then started a small bible study group using it as a starting point. We have watched the first episode of the second series and decided to be more cautious about it and not show it to the children without previewing it from this point. We intend to watch the remainder of the second season sometime soon.
It's a very well made and interesting series. I think it captures the humanity and personality of Jesus very well. It also does a good job of reconciling the differing accounts of the choosing of Peter and Andrew, and the miracle of the fish, into a single plausible narrative.
However, in bulking it out to make a TV series they obviously have to add a very large amount of fictional content. Usually this is plausible, but sometimes it is questionable. One small detail I didn't like from the first series (don't open if you don't want the spoiler):
They also mess up the order of events in places quite seriously for the purpose of their storytelling.
I am also very cautious about it because the producer is the son of the man who wrote the Left Behind series, and there are so many serious theological problems that series promoted in our popular Christian culture, that I am wary that the Chosen could do the same thing. It is so realistic that once you've watched it, when you picture a certain character from scripture, you can picture the character as portrayed in that series, and that may introduce inaccuracies in your understanding.
But it is well-meaning and could do a lot of good, if used evangelistically.
I have found that when showing it to people who are less familiar with the Gospels, you have to be careful to point out which details are scriptural and which are not. There are some great scriptural details of people's lives that are portrayed really well - but if you don't already know the story it's impossible to discern these from the other details that had to be invented to flesh out the character. Sort of like how the Lord of the Rings movies only really make sense when you've already read the books, but more extreme.