LondonGenie said:
I wouldn't give long odds on a "reasonable person" reading that and coming up with a unified, complete understanding.
My guess is that the average desk jockey would be able to read into that whatever they wanted to get out of it. If they don't like the cut of your jib, they won't let you in. If they think you're a good bloke, they'll pick one of the many exemptions.
Of course, a lawyer or senior bureaucrat could come up with a completely different interpretation.
On a practical basis, unless your name is on a computer database, or you admit to a conviction for an act of moral turpitude, you will be admitted. I doubt that we send the Yanks lists of every adult Aussie conviction, so what they keep on record would be US crimes, or lists of terrorists, or Interpol alerts.
They can't keep too many details on file, otherwise there would be so many false positives (your name is the same as a cat burglar) and false negatives (you changed your name to Unique Innocent and it shows up on no lists, even though you have a string of catburglar convictions under your previous name) that the system would be useless.
Mind you, if they pull you up for some other reason (maybe you are trying to evade customs duties) and they go looking back into your past with inquiries to Australia, all bets are off. They'll find any dirt if it's there to be found.
My experience, and I've entered the USA six times over the past couple of years, is that they take your card, look over it to see if you've declared any misdeeds, they scan your passport (which presumably brings up your name) and if no bells ring, you are OK. They also take thumbprints and photograph, but I doubt that these are used for any sort of instant biometrics search, but rather they can file these away for later use if need be.