In my time with the game, it only crashed once, and I have certainly had the original versions crash way more often. I would see things occasionally floating in mid-air, mammoths magically drop out of the sky, etc. The Nintendo Switch didn’t escape this either, but for the most part, it was just amusing stuff. Skyrim is also a massive open world game, and every version has had some bugs. But that’s always been true, so if it didn’t really bother you before, it shouldn’t be a problem now. A lot of the colors are drab, the character models are dead-eyed and stiff, etc. Admittedly, against more modern games like Legend of Zelda: Breath of The Wild, which was heavily influenced by Bethesda’s open-world RPG, you might notice some things didn’t age all that well.
But yes, Skyrim looks and plays on the Switch like a little smoother version of the 360/PS3 versions. Skyrim is a six-year-old game that while very impressive for its time, ran pretty well on the Xbox 360, so it running well on the Nintendo Switch isn’t that impressive of a feat.