Honestly, I'm not sure how much feedback you're going to get on this forum since most posters reside in North America and therefore aren't acquainted with the Aussie system of postal codes.
I can only relate how it works for me in Canada. If I navigate to-->address-->zip code, I initially see a Canadian flag as that area of North America utilized for my last navigation. I don't believe your Aussie map comes with the New Zealand as well, does it? If not, then it makes sense to show the Aussie flag as that is the only map installed.
(If I want an American zip code, I first have to tap on the Canadian flag and then I see a choice of US States to select from. An interesting question is what if I don't know what State. Then, essentially the function is useless).
For Canadian postal codes, like British (and I think Aussie), the code is a combination of letters and numbers like this: ANA NAN. The 720 is set to only use the 1st 3 characters (ANA) unlike the British file which, to my understanding, narrows down to 6 or 7 characters. So, for us, once we key in ANA, we then have to decide on a street in that general area .... again, not too functional.
And, yes, when I key in the first character, if there is no 3 character combo in the file starting with that letter, then I'm presented with cities in various provinces starting with that letter.
As to your reference to a street in a different city .... earlier NA maps suffered from the equivalent thing, if I understand you correctly, in that I would actually have to first select what was essentially a suburb of a city that the street actually resides in. The cure for that, as such, was upgrading to a higher level map (in my case, 8.10 from 7.10).
Lastl, as to why your unit doesn't appear to recognize Aussie postal codes??? Perhaps the postal code file is corrupt. I know that the odd British poster in a Brit forum was able to be sent a proper postal file in an email from British TomTom support.
Perhaps a pin reset? Or, nothing to lose, try the Clear Flash tool from here:
http://www.tomtom.com/support/index.php?FID=6211&Lid=4
or, a bit more drastic, reset to factory settings.
Make sure you do a full Explorer backup prior to doing the latter ... just in case.
Finally, have you called TT Support in Australia? The number is: 1300 135 604.
Good luck.