Our umpires are not professional (they all have day jobs) and the same three field umpires never work consecutive weeks together. This is where the major problem lies. They can never get any continuity, and as each umpire interprets different rules in different ways, it is the players, and the spectator, who are left scratching their heads.
Interesting.
NFL referees used to have regular jobs as well. Some still do, but it's far more rare now. The league decided that, to get the most professional performance out of it's officials, it had to PAY them like professionals.
As I'm sure you know, they also work as a crew, and that gives them the opportunity to work just like any other team of people. They understand what the other guy is going to do, what he's going to be watching for, and when he might need help.
The head of officiating for the league reviews every officials' performance every week. Occassionally there are penalties handed out for poor performance, such as what happened to highly-respected referee Ed Hochuli a couple years ago. The highest scoring officials for the season work the Super Bowl, so that's a nice incentive.
Now...and there will be some disagreement with this, but I also think instant replay is great. It's taken a number of years to refine it to the relatively efficient system it's become, but it's an effective tool that doesn't distract too much from the game. Although I'm not sure how well it would work with "judgement" or "interpretation" calls as you describe in Aussie Rules, but there might be something that could be done.
Frankly, I would have a hard time enjoying a sport that didn't have consistent officiating. It almost becomes like pro wrestling if the officials themselves don't agree on the rules.
(Speaking hypothetically, of course. I'm not saying that's how it is. I don't know. Just saying that's how it might seem if rule interpretations vary too much.)