Static recompilation of Majora's Mask (and soon Ocarina of Time) for PC (Windows/Linux) - Zelda64Recomp/Zelda64Recomp
Zelda 64: Recompiled is a project that uses N64: Recompiled to statically recompile Majora's Mask into a native port with many new features and enhancements.
Like the Mario 64 recompilation, this isn't running on an emulator, but is totally native. That means it runs smoother, has zero issues that you might get from emulation (like inaccuracies), and makes it so much easier to mod and extend it. You can see some of the features on the page like autosaving and playing on high framerates.
Also much more possibilities in terms of controls, ie no more janky remapping buttons and mouse axis into pretending to be controller inputs or messing with mouse injectors, instead you can get native KB+M support, dual analog, etc.
Emulation is almost never 100% accurate, that's why seemingly perfect emulators like Dolphin still get updates. They mimic the original hardware as closely as possible but there are still bound to be some bugs and games that don't work perfectly. The best emulators are more like 99.9% accurate.
N64 emulators aren't that good, so you'll get occasional graphics errors and crashes.
100% accurate emulation is basically impossible for every single console. You can get extremeley close via cycle accuracy, emulating the CPU's instruction set but even that isn't perfect.
Software-wise, sure. It's easy to dump the BIOS and game. The hard part is emulating the hardware. Consoles often have quirky architectures and special chips that don't map to PCs very well. And the chips themselves often have quirks that either aren't documented, or work in a way that disagrees with documentation. But the game developers often relied on those particular quirks for their games. For example, if there was a bug in the GPU that caused textures to become blurry when loaded in a certain way, a developer might exploit that as a free blur filter. (If you're interested in actual examples, try the Dolphin dev blog. I think it's really interesting.)
The ROM in this case is only used for game assets, like maps, models, and textures. All the game logic in native code. This allows is to be easily modified to add in new features without trying to hack it into a 20 year old game/console.
It's a bit similar. However this goes a bit further than I understand those projects do. They're creating a game like the original. With this decompilation project, if you use the N64 compiler you will get a ROM which is 100% identical to the original.