Early on Ted says "You slave away to the needs of your parishoners and what do you get? A one-way ticket to Palookaville." This is a reference to the famous taxicab scene from On The Waterfront.
In an early scene a woman leaves a baby at the door thinking it's Mrs. Riley's house and Ted informs her that it isn't. Ted then says to Dougal how funny it would be if they would have had to look after the baby which would have been similar to 3 Me nand a Baby given that 3 men live in the Craggy island parochial house.