I just thought of something: in that third season episode where Picard is replaced by a doppelganger, the thing which makes Riker twig that he isn't really Picard is that he leads Ten Forward in a rousing sing-along... something he knows the Captain would never do. Surely when Picard says "Do you know the words of HMS Pinafore?", Worf should be unholstering his phaser and asking "Who are you and what have you done with the Captain"?
Movie Picard ≠ Show Picard
Why do I see a difference between a rousing sing-along in Ten Forward which he never ever did before, and to sing one song where he explains that it will divert the attention of the android they're trying to catch?
Besides that, Picard has been shown to grow as a character. In the final episode of TNG, he joins the Poker game for the very first time ever. Over the course of the show, he started to like and get along with children. And more of that stuff.