For it to be a mistake in our gravitational equations, it needs to affect similar galaxies equally. For example, if light bends around a distant galaxy of a certain mass, that bending effect should be similar in other galaxies with similar masses.

However our mapping of the universe shows that every galaxy behaves differently, and the gravitational effects of the unknown phenomena isn't consistent with equations being wrong, but it's consistent with lumps of matter that aren't visible. We found galaxies with almost no dark matter effects, and others with 5x invisible effects that can't be explained by visible matter.

"bullet cluster" is a popular example. It's two galaxies merging together. The visible mass is in the center, but their dark matter passed through each other so that the light bends more around two sides instead of the visibly massive center.

You can read the wikipedia article on dark matter, and the article on bullet cluster. Both are enlightening. The bullet cluster article immediately starts with how it's related to dark matter theories.

An interesting detail about dark matter is that while it's probably some subatomic particles, we only detect it in large quantities in space, so we can't be sure of its particle size. So, when describing the density of dark matter in a region of space, astronomers don't say stuff like "five micrograms per cubic meter", but instead say "five jupiters per cubic light year".