Over all the article is cute and there are a couple laughs though there are also so many missed opportunities. Here is a play by play and a few suggestions.
Intro: Political in joke is funny. I think you can come up with a funnier false link than "idiocy". The last couple sentences are funny though the last line is sort of expected. You could think about taking it in a different direction such as "however these days a nations finance minister is expected to be incompetent. In that sense, Australia has the best Finance minister in the world".
Early life: This section is cute and maintains the ironic jabbing tone, though its written a little awkwardly and a slight bit confusingly as well.
Political life: I would suggest adding "to those below him" in the threatening sentence, as otherwise it wouldnt make sense (you cant threaten people above you on your way up). Someone slowly working their way up would not be threatening people above them, or maybe I'm wrong. The second paragraph is quite weak. Its not that funny and also awkwardly written. Consider taking each paragraph in a different direction. The humour as it is in this whole section is sort of just saying, this guy is a typical politician who is corrupt and a bit of a scum bag. You could add a whole new concept to this (maybe he is waiting to become PM with a hidden agenda (communist, socialist, radical capitalism, to welcome aliens from another planet, to invade New Zealand, to become a film star) or he could be forced into these positions against his will such as: After several ins and outs he was forced into higher positions kicking and screaming. To his great ire, his caucus punished his good and sensible politics by voting him as deputy prime minister. The biggest sourest kick in the face was also giving him the important role of Finance Minister, something he would never forgive". In any case, I think this section and the whole article would immensely benefit by adding an additional angle to the article other than simple, this guys yet another dirty political figure. You could go with the whole "he was forced into politics" angle, rather than he is just another dirty politician.
Rudd: Seems like more of a wikipedia article than an uncyclopedia article. The only distinction are the fake links. I cant really advise how to deal with this as I dont know much about Australian politics.
Gillard: Here, darker side of the party is an interesting idea, but it should be developed. What is the darker side of the party? What do they do? How was he sucked in? Theres so many places you could go here. The photo thing could also go places...other than rape. This could also be a whole new theme in the article, instead of rape, he could simply be madly in love with Gillard. In fact that could be yet another angle of the article to develop. This section is cute, but needs a lot more work to bring out humour or lols.
Opposition: This is also a rather weak section. The humour is all based on him being a phony politician and sucking at everything he does. Again, you bring up many themes: him fucking up, hating politicians, being a loony, boat people...but you dont develop any of them and this is why there is little laughing (at least from my part). You could easily take just one of those themes and write the whole section on it. Develop it all beyond more than just one sentence for each idea.
Controversy: Nice first line. I like the china sentence as well as with the final paragraph. This is the best section by far, though it could still use development, as is the case with the whole article.
As I have pointed out in the humour section, the concept seems to be: This guy is an ass hole. Here is reason 1, reason 2 and reasons 3 through 20. A lot of them being slightly cliche. The last section was one of the only places where you took an idea (carbon tax) and took it further than just a sentence. I would recommend either basing every section on one of these ideas (him becoming the finance minister, his love for the PM, carbon tax etc... and sticking solely to that theme and developing them much further, or writing the way you have but with an over all theme behind it, such as the "he never wanted to be a politician in the first place and was kind of forced into it" idea that I gave. In any case, you should decide what you will do, develop each section with just one idea or infuse an over all theme into each of the ideas...and then rewrite the article in that way, and single mindedly so. Go over the whole article with just that one concept in mind and dont digress too much. The article will greatly benefit from it and become a lot funnier very quickly.
A second note, I read this article as someone who knows nothing about Australian politics except that there is a woman PM and I feel that I haven't really learned anything new or know anything more. I would suggest toning down a little on the Australian in jokes and consider the wider audience when writing it and use this chance to teach them a little about Australian politics. There is no reason why someone wouldnt enjoy an article about the finance minister of some other country, but do consider the majority of uncyclopedias readers (if we have any) when writing.
So to sum up, try to take it easy on the "this guy is a total idiot and fake politician" and try to explore more of "why" he is that way and how he got there, and why a reader from outside of Australia (or from Australia for that matter) would care.
Prose and formatting:
Most of the article apart from concept and humour is well written except for the two confusing moments mentioned above. Im the worst person to consult for grammar and spelling.
I like the first image and the caption. The second is by far the best moment of the whole article. Very creative, but I really dislike the caption. Rape in my opinion should either be treated as an entire article or section or not at all, its really hard to make a good one liner rape joke. I would suggest going with the, he is secretly in love with her and thats why he stayed in politics idea or something of the like. The third image is okay and the caption is kind of cute. Consider adding other images such as someone handing someone money, a picture of an abandoned factory with a caption "Lets just throw money at an environmental problem and hope it will just go away". He doesnt have to be featured in all of the images.
This article right now is about a six.
I think you have a bunch of great ideas waiting to be expanded and developed on. Hopefully you can explore some of these further or fit them into a more consistent structure. If everything was written more like the last paragraph and with the creativity of the black and white image, you will end up with a great article. GL!