Update: July 2014! - See movie, below. The case of the mysterious appearance of Barramundi in Sydney Harbour has been solved.
Australian Museum web expert, Sascha Schulz wrote:
There were several Barramundi spotted, both on the south side near Rose Bay, in Darling Harbour and near Manly. Comparison of scale specimens from a fish speared in the harbour, with scales from shop bought fish suggested to me the Barramundi swimming around Sydney were originally from fish farms. But I had nothing to back that up at the time.
A month or two later investigations by NSW Fisheries revealed that local Bhuddists had been purchasing live Barramundi and other species from fish retailer and releasing them as an act of kindness.
Generous though this act seemed, these fish are not suited to our climate and would have perished after a short time. The people responsible were not charged with anything, but fisheries officers did explain about the risk of introducing parasites and disease to local waters, as well as the futility of the releases. Once this was cleared up the practice stopped.
Post script. 23 July 2014. The practice appears not to have stopped. Krystof Tichy filmed the above movie under Sydney Aquarium. It shows a very unhealthy Barramundi.
View an early movie of a Barramundi in Sydney Harbour.