"Fact 6" makes no sense

This movie takes QUITE many liberties with what it tells us and what it shows us. What I mean is, it tells us this guy can't make new memories, YET he acts as he can remember a big bunch of stuff since the incident anyway. It tries to have it both ways.

Of course if it was at all realistic, we wouldn't have a movie, because Leonard would just 'wake up' every 15 minutes or so, remembering only the incident and his wife dying.

He would not remember his 'investigation' or whether the police believed him or not, he would not even know he has a case file, he would not know he has tattoos until he checks, and so on.

Realistically, Lenny would be exactly like that guy that this actually happened to, I .. eh.. forgot.. his name, but he used to be some brilliant musician and composer, you can find him easily. That guy just lives the same moment endlessly, because he forgets the previous moment, so there's NO WAY for him to be organized, or even coherent enough to realize who or what he is or what he's trying to do.

He could not have any goals, let alone be successful in murdering people.

Considering all this movie tells us about Leonard's condition, it just makes no sense that he is so organized that he even numbers his 'facts' he wants to tattoo on his body. He shouldn't remember that he even practices tattooing his body, or who John G. is without checking those tattoos.

How the fjord would he be able to summon the EXACT right fact number out of his memory (!?) when writing down Teddy's license plate? How does he know it's 'Fact 6'?

HOW?!

Please make that make sense to me.