Frequency/harmonic analysis of accents
I would guess that the most prevalent difference between accents (of the same language) is how the vowels are pronounced. Humans distinguish vowels mainly by the frequency of the formant, i.e. regions of high energy in the harmonic spectrum. 

A good way to display this is the "formant map" which plots the frequency region of the second formant against the frequency region of the first. See for example: http://www.phy.davidson.edu/fachome/dmb/digitalspeech/formantmap.gif

In this 2D map every map has a specific region. For different accent the centroids of this regions probably shift around. That is certainly true for different languages. An interesting approach would be to measure this map for, say, an Australian vs. an American English speaker and look for systematic differences.