The short-term impact is that people are encouraged to give the Church another look. It's up to the liveliest parts of the Church - the dynamically orthodox parts of the Church - to seize that opportunity.
I'd also hope that my liberal friends, who find in this pope a critic of what they're pleased to call "culture-warrior" Catholics, will read carefully, and ponder even more carefully, what Pope Francis had to say about the "ideological colonization" implicit in Western decadence when he was giving robust pro-life, pro-family talks in the Philippines.
There's the trope about an impending "global-warming encyclical." The pope is preparing an encyclical on nature and the environment, including the human environment (which includes the moral imperative of a culturally affirmed and legally recognized right to life from conception until natural death). So what happens? A low-ranking Vatican official for self-promotion gives an interview to the Guardian in which he claims that this is a global-warming encyclical - which he couldn't possibly have known, as the document wasn't drafted yet.