“The Finest Hours,” which was filmed in Chatham, Cohasset, Duxbury, Marshfield, Norwell and Quincy during the summer and fall of 2014, bought or rented goods and services from more than 1,300 Massachusetts businesses in 155 cities and towns during the time it filmed in the state. The crew spent $1.7 million on hotel rooms and created scores of jobs, and boosted tourism, according to the MPC.