A few of the cases covered:

• Tatl the fairy’s information on a couple of the bosses changes as you progress through their fights.
• The guards blocking the exits to Clock Town usually use the presence of your sword to determine whether they will let you leave, but if your sword was stolen or is being forged they’ll notice and let you leave anyway. They also give you different hints on which dungeon to do next.
• The Astronomer has special dialogue if you speak to him as a Goron or a Zora.
• The residents of Clock Town each have their own little story of how they’re handling their impending destruction. The Swordsman especially has interesting reactions that change as the clock ticks down.
• The Swordsman also, like the Happy Mask Salesman, has a reaction to every mask you can wear to his shop. The lady in the Treasure Chest game and the both the proprietor of the Trading Post and his employee have unique reactions to some of the masks.
• If Deku Link can shoot bubbles they can play the archery game, not even needing a bow!

What’s great about all of these cases is none of them are necessary to win the game! It’s there for the players who try to experience Majora’s Mask’s story from every angle. Disable used a text dump to chart out all of the game’s dialogue on a web page here.

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