Joker was in the area and was hiding.
The police kept him in the area because of their massive presence, but they couldn't see him. Not being able to see him, they couldn't know for sure if he had entered a home in the area, and the only way to know is to go house to house and contact the residents.
When night approached, they police decided to leave.
Then the citizen spotted Joker.
If the police had not had the numbers in the area, they would not have subsequently captured Joker.
So far, I have not seen a satisfactory answer about what they could have done differently.
Wrong again. They had 9000 cops in the area. They violated the 4th all day long then held a news conference and stood down to a fraction of that number (officially they said Watertown plus an equal number of state troopers but they probably had more). It was at that point that the citizen called 911.