The short time constraints they gave him and therefore the crew to produce these massive movies. The ultimatum/threat that if he didn't direct, they would get someone else AND they wouldn't film in New Zealand, but instead a studio backlot.
He initially signed on for just 1 movie, then they expanded it to 2 and then right before the first one released, the studio decided to make it into a trilogy to get more money. The studio had to share profits for the first movie with all the other studios/production companies that had a hand in the rights to The Hobbit, but they were for only one movie. So WB wanted to get their share and then some, therefore expanded first to two movies so they would get all the profits from the second, but then wanted more money and expanded to 3 movies. So, the first movie had to be re-edited right before release to end differently than originally intended.
No one was ever ready when the cast arrived to shoot their scenes b/c things were constantly changing whether that was from Peter or the studio. Sometimes the cast would show up and they would just decide not to shoot them that day and instead do something else. From what I remember, they said the main Hobbits had no stunt doubles (only body doubles for certain scenes) which was challenging for some of the older cast members when it came to doing stunts.
After the success of the Hunger Games, the studio wanted their own bow and arrow beauty which is why Tauriel was created. Had nothing to do with Peter apparently.
Lots of other stuff that I'm not remembering. It's a great little documentary though if you can catch it. It was on the channel Vice. They have other ones in the series as well for Batman, Star Wars, James Bond and even The Fast and the Furious