‘Broadway Danny Rose’

This 1984 winner finds Woody Allen at his most irresistible. Allen casts himself as a doggedly persevering small-time Manhattan talent agent, representing acts that supposedly went out with vaudeville. He crosses paths with a blond gangster’s moll (a wonderfully raucous Mia Farrow, virtually unrecognizable with dark glasses and a Brooklyn accent). It’s a pure joy from start to finish (A&E; Friday at 6 and 10 p.m.).