The most common complaints about online poker sites in Australia are very much the same as players in other countries will face when they're looking for a game. Most often, any complaints are related to the quality or response and resolution speed of customer service, game fairness and the idea that games may somehow be rigged, or payment processing issues.
For each of these, and usually irrelevant of the poker site concerned, it's often a misconception or misunderstanding on the part of any player that's at the root of the problem.