The rotation curves of galaxies unexpectedly flatline beyond the extent of their luminous matter. While this is conventionally interpreted as a sign of dark matter, it may instead be due to a breakdown of Newtonian gravity in the relevant regime. This possibility is bolstered by the very tight correlation between kinematically inferred accelerations (e.g. from rotation curves) and the expectation of standard physics (visible matter only + Newtonian gravity):
Article One Law to Rule Them All: The Radial Acceleration Relation of Galaxies
But perhaps it is really just due to dark matter. That's what I thought, until I came across the satellite plane problem. Basically, this is the issue that the Milky Way's satellite galaxies mostly lie in a thin plane and co-rotate within it, with the same being true for Andromeda. This by itself isn't necessarily a problem, but the only real way to get planes of satellite galaxies this thin is if material from the host galaxy's disk was pulled out by a tidal interaction. It could then settle into a disk inclined to the original disk. It's essentially the same argument for why we know there must have been frictional processes when we see the Solar System is flat. As the hypothetical dark matter isn't frictional and the baryons are, it makes sense to have satellite planes. We sometimes see them forming out of tidal tails elsewhere (e.g. in the Antennae). The problem is that it leaves the satellite plane members (tidal dwarfs) with no dark matter and thus with very low internal velocity dispersions. This contradicts the high observed internal velocity dispersions of the Local Group satellite planes, as discussed in this recent review article:
Article The Planes of Satellite Galaxies Problem, Suggested Solution...
If these high velocity dispersions aren't due to dark matter, then logically they are due to modified gravity. I've tried to explain this and some other important reasons why I think gravity is modified in this lecture I gave:
https://www.youtube.com/watch?v=PYVC0VtmpDg
My YouTube channel has some more recent videos looking into some more technical aspects - the most recent one into simulations of the satellite planes forming in modified gravity (MNRAS, 477, 4768) and the one before that into the positions and velocities of more distant non-satellite Local Group galaxies, doing what is called the 'timing argument' in a conventional gravity + dark matter context and giving an idea what might happen in modified gravity (MNRAS, 473, 4033).
Anyway, I wonder what you thought. Can General Relativity really explain everything? We know that assuming it does implies dark matter - are you happy with this? Or do you just feel uncomfortable tampering with equations written down by Einstein, even though no external galaxies were known when he did so and the rotation curve of our own one was not known?