I found a plot hole, but I've filled it in on my own rather well. It still poses potential problems though, as my solution might conflict with later details that will be revealed to us.

In canon, Voldemort learned how to make a Horcrux from library books. HPMOR added the Interdict of Merlin, which means that this couldn't have happened. The Interdict of Merlin means that Voldemort could only have learned how to make a Horcrux from a living person. At first, I thought that this broke the story. But then I found a solution.

The solution is that Voldemort must have broken into Nurmengard sometime before making his first Horcrux, where he would have extracted the information from the mind of the imprisoned Gellert Grindelwald. I think that should be possible, and it would actually fit very well from a thematic point of view as well.

However, there's the possibility that it would conflict with whatever backstory Eliezer has in mind for Quirrel's identity as the supposed last scion of an ancient house. Also, it limits the paths this story can take, because through my solution would give Voldemort knowledge about many of Dumbledore and Grindelwald's secrets, such as the existence of the Deathly Hollows, and it also makes Voldemort even more OP'd.

This comment exists so that we don't end up with a major, unfixable plot hole later on in the story.