A Coast Guard form (reporting weather and shipping messages) shown in the lighthouse scene lists the Coast Guard as part of the Department of Transportation. The Coast Guard was under the Department of the Treasury until 1967.
One scene shows a Coast Guard Petty Officer wearing a peacoat. His peacoat has his insignia of rank (red chevrons and white eagle) on the outside of the left sleeve. The US Navy and presumably the Coast Guard did not adopt the policy of wearing the insignia on the sleeve of the peacoat until the mid 1960s.