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Executive Meddling / Troubled Production: Let's see where to start:
The first problem emerged in 2008 when New Line Cinema and Warner Bros. refused to pay the Tolkien Estate the money that they owed them (including for The Lord of the Rings). What followed was two and a half years of everything spiraling out of control, not only sending the film into Development Hell but causing Guillermo del Toro and some of the actors to leave production after having been attached to it. To make matters worse, these legal issues got so bad that it would have taken the production out of New Zealand entirely. Only when Peter Jackson decided to come back to the director's chair in late 2009 was everything sorted out.
And then the studio only gave Peter Jackson and Weta six months of pre-production and told him to start filming immediately afterwards or else (for comparison, the Fellowship of the Ring alone had in pre-production for a little over two years before filming began). And before production could even begin, Jackson was hospitalized in January 2011 for a perforated stomach ulcer, which eerily was one of the contributing causes of Tolkien's death. Luckily, it was caught in time and surgery went smoothly. This, however, forced production and principal photography to be halted for a month.
Filming itself went smoothly for the most part until the decision was made to split it into three movies instead of two. The sound designers, mixers, and editors had to create and edit new sound effects halfway through doing the second film. Then there was the decision to CGI Azog, Bolg, and the orcs in the first and second films, with the decision with Bolg being made so suddenly that whole sequences had to be re-shot, which is why in the trailers Azog is the one chasing the dwarves◊ but in the film it's Bolg. The scene where the group tries to bury Smaug in gold in the forges was added only because the filmmakers needed a cliffhanger, and the actors and some of the crew literally had no idea what they were filming until the finished film.
When it finally came time to do the third film, the studio practically took the film away from Jackson and forced him to edit it in a way he didn't approve of and imposed tons of baggage onto film, demanding more emphasis on the love story and possibly more Alfrid scenes (due to Stephen Fry not being available anymore to play the Master of Laketown gain). The Battle of Five Armies had to be until the end of shooting because they couldn't find any locations in New Zealand that would've worked and because the battle turned more complex through the development of the films.
All of this ended up blowing up in Warner Bros' faces. While the trilogy did overall do well financially, it became divisive for audiences and critics (with the third film, the one that reportedly received the most interference, becoming the lowest rated and lowest performing Hobbit movie at the box office), and the Tolkien Estate has relinquished the film rights to the books until further notice. All the aforementioned meddling was confirmed not just by Peter Jackson, but also by Graham McTavish and Evangeline Lilly, with McTavish confirming the theatrical cut for the third film isn't what was intended and that the extended cuts of all three films are closer to Jackson's original intention.
Crosses into borderline Tear Jerker when, according to a fan, someone asked Jackson at the premiere of the third film if he was going to see it. He said "I will but not yet. I'm not sure what the studio has done with it." Fortunately, he later gave a better review of the extended version, which he declared himself proud of, even if he admitted that still it wasn't devoid of Executive Meddling (for instance, they cut ten of the promised 30 minutes of footage without Jackson's permission)
In a more humorous example of Troubled Production, Christopher Lee loved telling stories to the production crew while filming his part, to the point that it was slowing down production on that day.
The Tolkien Estate's refusal to allow Jackson access to Unfinished Tales of Númenor and Middle-earth and The Silmarillion resulted in a lot of changes having to be made to the lore, most notably the backstory of the Nazgûl.