I wasn't specifically talking about Majora's Mask.
I don't know how to explain how important emulation accuracy is to me, but I will try my best.
1. Many Super Mario 64 hacks can't run on a real n64 because they make inaccurate hardware assumptons.
2. Games like Pokemon Snap and the 64dd games are unplayable on less accurate consoles.
3. Accuracy in emulation allows for tool assisted replays to be run on an actual console.
4. Although meant for the snes, http://byuu.org/bsnes/accuracy">this article should explain some things. Pity it's incomplete though.