The main thing I had remembered about the series as a whole was that the third book didn't work as well for me as the first two. Now I have a much better sense of why, and this review of the series really sums it up for me (the review is overall very positive, and contains a lot of spoilers).
...[T]he last few chapters, where Pullman realizes that he’s set up this entire theme that can only be resolved by having a 12 and 13-year-old fall madly in love... unravel a bit as he both hurries through the unconvincing love scenes and then comes up with a tragic ex machina to separate them so that they can grow up and love other people, too. It’s too bad, because I appreciated the grander idea behind the final scenes, which is that the concept of original sin was not sexualized by accident, but instead was a tool to poison people’s intimate relationships with misogyny and shame, and cripple our collective development into better people.
This is exactly what bothered me. I appreciate and agree with Pullman's point that the repression of our sexuality as a natural part of our humanity, whether by the church or any other cultural forces, is bad. But the salvation of the universe resting on Lyra and Will discovering themselves as sexual beings was too literal for me. Never mind their ages; even if they'd been adults, it would've been an issue for me. I'm also less than impressed by the suggestion that awakening sexuality is, by itself, the path to adulthood. Coming of age is so much more than that.
All that said, I still enjoy the series a lot and recommend it to anyone who hasn't picked it up yet. And I look forward to seeing what Pullman comes up with next.