If his Aussie passport is his first, he'll need to show his Thai birth certificate when departing Thailand.
He can return to Thailand visa exempt as an Australian citizen but he'll be 'overstaying' once the 30 days is up. Not a huge issue for a kid, as he cannot be fined or banned for overstaying, but if he leaves Thailand on that passport it will be stamped as 'overstay'. If he attends an international school here, they may insist that he's not on overstay.
Of course, if you can get his Thai passport sorted, it will solve a lot of problems!