Does anyone know why the time in Adelaide, Australia is half an hour different to the rest of the world?

I think you meant to ask why Adelaide is 30 mins behind Australian Eastern Standard time, rather than the rest of the world? Easy...same reason Sweden is so far behind the Australian time zones: location. Australia is a huge country (Sweden is tiny) and Adelaide is a huge distance from the east coast, it makes more sense for it to be behind in order for the time to fit in when the sun is actually shining in the sky (and when it's not). Western Australia is further behind than Adelaid because of it's location also.