Oh, and that would be an “accent”, not a “dialect”. Especially the way he speaks it.
…and especially GECKOS!
Definitely Cockney.
Who are you who are so wise in the ways of insurance?
I don’t get it either, but I come from Essex, a place called Southend, on the mouth of the Thames, to the east of London, and when I first visited America I was several times taken for an Australian. (That was in the early '80s though, a time when many Americans seemed to be just discovering Australian culture. I did not get it so much when I came back to the U.S. in the 1990s.) I think I probably have some traces of Cockney in my accent, but I am pretty sure I sound nothing like the gecko, who has a true London accent.
Well, we were discovering Paul Hogan, anyway. 
Actually this 1983-4, a bit before Crocodile Dundee. I think there had recently been some other moderately successful Australian movies, however (I forget precisely which).
I know some Brits don’t like to admit this, but there are just enough similarities between some British accents and some Australian accents in ways that are different from most American accents that an American with little experience in either British or Australian accents could easily confuse the two. As I’ve said in threads like this before, people tend to overestimate the differences in accents which are close to their own and tend to underestimate the differences in accents which are farther from their own. Americans with little experience in non-American accents could easily confuse British and Australian accents. Despite the claims of Brits (in various threads on the SDMB) that there’s no resemblances among the various British accents (let alone some resemblances between British and Australian ones), there are such resemblances in ways that consistently differ from American accents. When an American says that he hears some resemblances between British accents and Australian accents, there is something real there that he is noticing.
Paul Hogan was featured in a very successful ad campaign for tourism in Australia (“Come ‘n’ say “g’day”; I’ll throw another shrimp on the barbie for yer.”) This raised consciousness of Australia in the U.S. to such a degree that I’m not surprised that an Essex accent was mistaken for Australian at that time.
Anecdotal support for this: I’m fairly familiar with British accents, and I have Australian relatives, but I still find it very difficult to distinguish Essex / East London from Eastern Australia / NZ. My relatives are in Western Australia, which is unmistakable to my ear, and Geordie / Brummie / etc. sound nothing like NZ / Aussie to me. (For an example, the casts of “Neighbours” and “East Enders” sound really alike to me.)
True in general, I don’t doubt, but some English accents do vary a lot from others. A strong Geordie accent, and certain Scottish accents, can be close to incomprehensible to people from southern England, who have no difficulty with either Australian or American English.
Mad Max, maybe?
The first two of those came out in 1979 and 1981. Thunderdome, the last of the trilogy, came out in '85. (*Crocodile Dundee * was in '86.)