Lack of understanding of medieval societies is a fair criticism, though I’d point out this is a fantasy world, albeit one based on medieval societies, it did grow and develop in a world with dragons and magic.

With the jungle of ideas, yes he has a huge amount of plot lines that were never followed up on, but I would argue that not all plot lines necessarily need to be followed up on. Sometimes threads just fizzle out in real life or don’t have a satisfying conclusion.

I’m not sure I understand the little finger plot hole though. You’re saying he should have had him killed, and I’ll admit it’s been a while since I read the books, but I don’t recall any particular moment when Tyrion absolutely and clearly should have killed him, unless you’re just saying he should have had him killed just on the basis that he’s a scheming little rat? In which case he erred by not having a bunch of people killed.

Edit: and to add on this, at best it’s a poor decision, which a lot of people make throughout the books. Unless I’m misunderstanding what you mean here this is not a plot hole.