Paint was thrown and a window was broken at Michael and Christine Bower's home in the Carnalea area of the Co Down town on 5 December.
The man is being questioned in connection with criminal damage.
A number of properties belonging to the Alliance party have been attacked in recent weeks, following changes to the flag policy at Belfast City Hall.
Nationalists on Belfast City Council wanted to stop flying the Union flag altogether, while unionists opposed the move.
Alliance, which holds the balance of power on the council, put forward the compromise which saw the flag flown on designated days.
Protests have taken place across Northern Ireland in the wake of the changes.