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It appears to miss a mouseClicked() event occasionally. I think its because mouseClicked() is way too sensitive to mouse motion whilst clicking. I may one day spend time faffing (yes its a real word, its just not in the dictionary yet) with mousePressed() and mouseReleased() to spot whether it was pressed and released in the same square. Till then, click repeatedly till it catches.

Sources are TicTacToe.java , TicTacToeBoard.java and HandleButton.java