Sounds like my 5 1/2 year old, too! And I will echo James Snell in that it seems like it's a pretty normal 5/6 year old thing. My son could watch the same episode of Octonauts or whatever a thousand times and pick up new stuff each time he watches it. I can remember being 6ish years old and vividly remembering certain dialogue or scenes in a movie, only to watch the same movie YEARS later and realize how little I actually understood the overall plot of the movie. At this age, it's really up to you to help him make those bigger connections and discuss them with him at a level that is appropriate for him.
From what I remember about being a kid and what I've observed in other children, I really feel like the late 7's/8's is when kids start making some of those bigger connections on their own, and some of those connections you've been hammering into their heads really start to sink in and click. Piaget suggested that it was around this age (7ish or so) that kids reach their concrete operational stage. They begin to demonstrate more logical, concrete reasoning and become less egocentric. There's been some debate about Piaget's theories recently--especially in regards to cognitive development in the pre-teen/adolescent/early-adulthood years, but his theories are still a pretty decent starting point for child cognitive development.
For now, I wouldn't worry about him focusing on the details--especially when it comes to things like Bible stories. Ultimately, he's going to hear those same stories a hundred times and every time he hears them he'll remember a little more and a little more. When he gets to the age where he can grasp that bigger picture, he'll all ready know the story and the bigger meaning will (hopefully) have that much more meaning to him because of it. For example, my son knows the Lord's Prayer and most of the Apostle's Creed. He recites them with us in church every Sunday, but he has zero idea what it all means right now. That's ok. One day he will be able to understand all the complexities, but right now I just want him to get the words down. It's harder to memorize stuff like that when you're 12 than it is when you're 4/5/6.