Take at look at this thread:
http://www.frequentflyer.com.au/com...stoms/visa-waiver-program-to-usa-6431-24.html
I have just posted a lot of information regarding findings of guilt with no conviction and spent convictions. Although it is regarding NSW you would be able to find the same relative legislation for your state which would be similar.
In short a finding of guilt becomes spent as soon as any fine or penalty (Good Behaviour Bond) is complete. Any other conviction becomes spent after 10 years of crime free period, from the last conviction. Some convictions however are excluded. I.e ones of sexual nature or involving minors. One a conviction is spent you do not have to disclose it to ANYONE and it no longer forms part of your criminal record. Although the act in NSW does not cover arrests, someone can still legally ask you about being arrested. You may choose to disclose it even though there is no way for them to find out unless having access to your criminal history. This is different to your criminal record and foreign agencies do not have access to this.
As to the previous poster:
You travelled to the US in 2006 without a problem. If your online ESTA says you are approved to travel I would not worry about the visa as in all honestly your chances of getting one are probably not great.
If you go off the Australian Traveller guide to travelling to the USA it says:
"Australians with a criminal record (regardless of how minor or how long ago the offence took place) should ensure they seek advice about their visa requirements for entering or transiting the United States as they may be refused entry."
You had a finding of guilt, which does not form part of your criminal record, therefore you should not be required to seek advice from the consulate.
The website also has a frequently asked question that asks:
I was arrested/convicted of a crime years ago. Can I use the VWP?
ESTA will assess your eligibility for travel to the United States under the Visa Waiver Program. The assessment includes questions regarding previous arrests and/or convictions. If you have been arrested for or charged with a crime, including offences involving drink driving or the use of a controlled substance, you may require a U.S. visa and, in some cases, a waiver of ineligibility. If you choose to apply for electronic travel authorization via ESTA, the system will advise you whether you must visit a U.S. Embassy or Consulate to apply for a visa.
It says the system will advise you whether you MUST visit the embassy. If you fill out the ESTA and tick no to all the questions and If the ESTA says you are authorised to travel then IMO there shouldnt be a problem.
As to the OP your arrests are going to be the problem. I cannot say you are legally allowed to answer no to the question as the act does not cover arrests. It is up to you whether or not you disclose it. I can however say that you have a clean criminal record, therefore to effect you do not have a criminal record as all your convictions are spent. As per this and as per the Australian Travel guide you are fine to travel. As I said before your arrests form part of your criminal history, as do your spent convictions and foreign agencies do not have access to your criminal history.
This just my opninion from the research I have done regarding this topic. Do not take it as fact.
The USA of course would love to know everything about you. Especially information they cannot legally obtain without you disclosing it to them.