> Why does it have to be this "Dark Matter" causing the mass differences we've been seeing? How do we know it isn't undetectable-through-normal-means normal matter, or aliens, or mistakes in our calculations/observations, or anything else?

"Dark matter" is just a name for "a phenomenon that only appears to interact with the rest of the universe through gravitational fields, and not through elecromagnetic fields, the weak, or the strong nuclear force". There are many competing theories for what dark matter actually "is".

The name is independent of any particular theory that describes its true nature, whether that's an exotic form of matter, aliens, or mistakes in our observation.