If you entered the US on a VWP, and try to reenter the US on the VWP without going further than Canada, Mexico or the Caribbean, you may find yourself denied entry.
I'm not sure if this applies if you were on a different class of visa before attempting to reenter the US using the VWP. I think the US border agents would be very suspicious though.
I've entered the US about 15 times since my E3 expired, and i'd say i've been specifically questioned about my E3 on 8 or 9 of those occasions. "You used to work in America? What's the name of your current employer? Are you looking for a job at the moment? You know you can't work in the US any more, right?" Stuff like that.
To be clear, I haven't had to deal with E3 related issues for 7 or 8 years and the subtle details of it have probably changed. Hopefully you never find yourself in a position where your E3 becomes invalid unexpectedly but if so, speak to a lawyer to find out the current gotchas and how US Immigration interprets the laws. (Or look at http://www.expatforum.com/expats/america-expat-forum-expats-... - it tends to be an excellent source of typically up to date information.)
Pro-tip for Australian's living in North America (or anyone crossing the Pacific, really): Qantas/OneWorld (and maybe other airlines) typically doesn't charge one penny extra if your North America <-> Australia route includes a stop in Hawaii. Hit up hotwire.com and find a cheap hotel in Waikiki and it's the absolute perfect way to break up a 14+ hour flight.
My parents are in Perth, so Emirates via Dubai is a slightly better option. Emirates are typically cheaper and their stock is nicer. Plus each of the legs is shorter than the trans-Pacific marathon.
Mind you, living and flying in the US brought an unexpected phrase to my lips: "I miss Qantas".
I'm not sure if this applies if you were on a different class of visa before attempting to reenter the US using the VWP. I think the US border agents would be very suspicious though.
I've entered the US about 15 times since my E3 expired, and i'd say i've been specifically questioned about my E3 on 8 or 9 of those occasions. "You used to work in America? What's the name of your current employer? Are you looking for a job at the moment? You know you can't work in the US any more, right?" Stuff like that.