“Their Finest is the sort of crowd-pleaser that knows the difference between satisfying its viewers and flattering them, all the while showcasing surprising performances from Gemma Arterton and Sam Claflin, and an entirely unsurprising one from Bill Nighy—a master scene-stealer pulling off yet another brazen heist—Variety. With London emptied of its men now fighting at the Front, Catrin Cole is hired by the British Ministry as a “slop” scriptwriter charged with bringing “a woman’s touch” to morale-boosting propaganda films. Her natural flair quickly gets her noticed by dashing movie producer Buckley whose path would never have crossed hers in peacetime. As bombs are dropping all around them, Catrin, Buckley and a colorful crew work furiously to make a film that will warm the hearts of the nation. R. 117 Min.