Slide down (pull down) for sync !!! Like Apple aps.

I would suggest to make sliding down a powerful multipurpose gesture, depending on your needs. It's function should be selectable in the preferences:
-Some people want to actively initialize the sync process. They could do it with an up-to-date gesture.
-Others want to avoid accidentally ticking off items. If this function is selected, items would first be crossed out and stay in place. Swiping down would clear the list and swipe all crossed-out items to the bottom list of recent items.

It always seems to me, between my wife and I, that when a shared list is changed that it gets pushed to the other device immediately... I'm not sure what more explicit sync options would really add here?