I guess there’s nothing wrong with it, but doesn’t it just do the same thing that the browser's “share” button does already?
I’ll probably never click it (just like I never clicked “bookmark this page” buttons), but if it encourages people to share the podcast more, then that’s good.
Side note: it works on desktop Safari too, although not other (Mac) desktop browsers.
Edit: After thinking about it, the button may actually be useful if it appeared next to each episode on the front page and on the episode list. It would be an easier way to copy/share individual episodes without having to click through to each one’s page or long-pressing the links for a context menu (or whatever other gesture your mobile OS of choice uses to copy link URLS).