We lived in Melbourne for 6 years and loved it. We were sad to leave and sometimes wonder if we've made the right choice. We've been back twice since we left.
Australia as a whole and Melbourne individually have problems, as does anywhere else in the world. On the racism thing, we were there during the period in which protests over attacks on Indian students and taxi drivers took place:
en.wikipedia.org/wiki/Violence_against_Indians_in_Australia_controversy
Friends of ours who are of Indian origin did feel uncomfortable and my OH, who worked in recruitment, did feel there was prejudice against Indian names. But, this was a good few years ago now. Things may very well have moved on.
I think the racism thing is a difficult one - I'm not entirely sure that Australia is any worse in terms of sexism or racism, I think perhaps people are more open with their opinions. I don't know. I adored Melbourne and can understand your reaction, SuperBeagle, to the comments about racism but all the same I can't dismiss them outright. Equally, I don't think the UK is an equal society by any means.
Culturally, there is a huge amount going on in Melbourne. I definitely don't recognise the comments about Australia being a cultural wasteland. We went to all manner of events, and friends are often posting about things they've been to. If you live rurally of course 'culture' is going to be difficult to access, same as in the UK. The food scene in Melbourne is phenomenal and I miss the restaurants hugely - fantastic cooking, available at all levels. We had so many excellent meals, and always felt they were great value.
On the friendship thing, well we were pretty young when we moved and for me in particular there was workplace socialising, in my first job at least. We made friends fine although of course they are never going to be friends who've known you since 3. On the flipside, these are people you are choosing to make friends with as a fully formed adult, rather than a friendship formed from a mutual love of mudpits or whatever, and in some ways I feel those friends are more 'me' than my oldest friends, if that makes sense. We did have a more expat friendship group than we do in the UK but that is probably more to do with the industry I worked in than anything else - and they were very often not British expats. We have plenty of Australian friends too.
There's no escaping how far away from everything Australia is, and we did come to miss the chance to travel inexpensively. We also missed family. We chose to move on to new adventures but like I say, miss it hugely and have questioned the wisdom of our decision several times. Still, we can always go back.