Games

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.

You can read this for more information:

https://emulation.gametechwiki.com/index.php/Emulation_accuracy

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.)

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.