I've only just listened to the beginning of the podcast and I'm only going to comment on the Head Boy James scenario for now. We don't have prefects/head boys in my country's schools, so I don't know what their specific functions are, but I am of the opinion being Head Boy requires different attributes than being a prefect. To be a prefect, I imagine a well-behaved, studious and rule-following nature would suit you best, because you will be responsible to keep other students in line and you'll need to give the example. But I think Head Boy would require, above all, leadership. I view it as a position that doesn't concern itself so much with the more mundane student problems, but with more important stuff and it probably also serves as a connection between the student body and the staff.
So, in the specific case of James and Remus, I definitely see Remus as suited for the prefect role, but not so much for the Head Boy one, as he didn't display leadership skills within his group. James, on the other hand, would be abysmal at being a prefect, but could possibly perform well at a position where his clear leadership skills would be needed.
I am also of the opinion that choosing James as HB was yet another clue of Dumbledore's instigator nature. It was during the Marauders' time at school that Voldemort's first rise to power was taking place and, even if open war wasn't happening, it likely wasn't too far from it. And students coming out of Hogwarts would undoubtedly be caught in it. Knowing Dumbledore, his choice of Head Boy and Head Girl would take this into account. I believe he saw in James the potential to be a leader during the war, but his wayward and irresponsible ways were an obstacle to this. Giving him the position of Head Boy would help him learn responsibility, mature and grow into the man he would need to be. And he would serve as an example to the younger students, as James was very popular and always strongly opposed to the Dark Arts and all that Voldemort and his followers stood for. In the same note, a popular muggle-born girl is the perfect choice for Head Girl.
Or maybe he just took matchmaking to a whole new level
On the subject of James and Lily dating, I believe they only start dating during 7th year and not before. But I agree with Rosie that the "incident" (which was during their 6th year, if I'm remembering correctly) would have had a great impact on James.
It's also possible that James' parents died somewhere during his school years and that affected him, but that's a whole new can of worms.
As for the chaser/seeker debate, I'm all for chaser!James. I don't think playing with a snitch has any relevance to what position he plays in. He's doing it to show off and you can't quite get the same effect with a quaffle, can you? You can't keep it in you pocket. (It's entirely possible that Jo changed her mind after the film, but I'm choosing not to believe it).