1. If your character has high enough intelligence, you're allowed to bypass certain puzzles (for e.g. mutagen puzzle, music cipher puzzle etc.).
2. You won't be allowed to do specific quests if you have too high of an intelligence. For example: some pipeworker tells you about a dancing skeleton, that is beating up kids and stealing their teeth and asks you to hunt him down, but your character doesn't believe him, because your character has too high of an intelligence, so because of that you can't do that quest anymore. In other words, your character thinks too rationaly, so he won't believe certain things (e.g. Forsaken Island Behemoth quest, your character would think that it's impossible for such a creature to exist, so you won't be allowed to do the quest, because your character sees it as a waste of time). Also there would be more uses for items or consumables which lower your intelligence. We could also make the opposite true, where if your character has too low of an intelligence, he wouldn't be able to understand some things, so you would then locked out of certain quests.