Score Keeping in Board Games: How Do You Deal with Independent Scoring?

We play a lot of games that require independent score keeping, such as Azul and Bunny Kingdom. These are basically honor system games, more so than general victory point games. Since the scoring is complex and completed round by round, there's no way of knowing whether the score is being calculated correctly for each person -- and, often, it just isn't. Over time, I've noticed that the same people tend to win these games, even if they aren't generally good at that type of game.
They aren't cheating.
They're confused.