Goood question my friend. As the resident KKJ fan, I'll do my best to help answer.
Ok, KKJ is the story of a high school girl, Maron, who lives by herself in this apartment complex with her best friend, Miyako. Miyako is obsessed with helping her father, the chief of police, track down an infamous thief of art called Jeanne. With your typical plot twist, Maron is actually Jeanne's alter ego, which makes life interesting between the two friends. Turns out that Jeanne is sent from God with a mission--to capture demons residing in different pieces of art. These demons have the power to possess the artwork's owners and make them do horrible things. However, when Jeanne seals the demon the artwork disappears, making her reputation as a thief. Add in a cute boy next door named Chiaki, a rival thief whom Jeanne suspects is working for Satan, a great plot and you've got the series in a nutshell.
Now this sounds well and good. The artwork, for example, is incredible, and the story had me breathless. However, I have to tell you some negative points too:
1. the story takes liberties with theology here. For example, Maron is the incarnation of Jeanne...which last time I checked wasn't possible in Christianity ("It is appointed for man once to die and then the judgement"). Also, the demons have the power to steal human souls and thus hurt God...they have a matrix-y view of humans as sort of spiritual batteries that can be used for God's power or the devil's. In the second season, things get really nasty theologically:
[spoiler] A demon, Queen, tells Maron that God forgot he was God and fell in love with a human girl named Jeanne (her prior life) and placed all his power in her, etc. [/spoiler] This was really unsettling to me, but a few of the lies they spouted I could accept as lies because they were coming from a demon's point of view. However, that's something you definately have to research and take up between you and the Lord
2. There are a few curse words. Also, the sub is...well not very great quality. Decent, but not superb
3. There is a little undefined nudity in the second season and a few bathtub scenes. However, if you can handle Sailor Moon or Magic Knights Rayearth, this shouldn't bother you too much
4. In the manga ONLY, there is an attempted rape scene. It's very mild, but it's there...this was way toned down in the anime series and made into a choking struggle and didn't even hint at sex.
Personally, I adored the series. I thought it was great, and I am mature enough in my walk to handle the bad things in it. However, I wanted to make sure I got that across to you right away. Here's the full review I wrote (
http://www.christiananime.net/forums/reviews.php?display=39) and of course, if you have any, any questions at all, please PM me. I'd be more than happy to answer them for you.