Haven't done it in an Australian airport, but I've done it at Calgary and will probably be doing it at Dublin, Prague and Budapest in the next few weeks. One advantage for me I guess is that I find it rather easy to stay up if I need to, so I will probably just wait it out until check in and then I can hit the lounge. I'll just make sure there's enough battery on my iPad really. I'm led to believe that some European airports allow check in the night before an early flight so I might be able to get rid of my check in luggage before settling in for the night, which would be quite handy.
When I did it in Calgary, there wasn't any major issues. The airport was open, but I'm pretty sure all the shops and restaurants/cafés were closed. There were a few vending machines selling the usual stuff though. The lights were on and the cleaners were working away, but didn't make a fuss about the temporary residents. There were a few others doing the same thing as myself, maybe 5-10 people. Not sure how one can guarantee that nothing will be stolen but I'm sure there are ways to reduce the risk, even if there is no luggage storage facilities.