I like it and plan to make it part of my already crowded line-up for Monday nights. And so far I see nothing that conflicts with the general atmosphere of Earth Prime-Time. This could really happen, tucked away up in Maine where it's outside the major concerns of characters living in other TV environs.
Characters in 'Major Crimes', 'Rizzoli & Isles', 'Perception', 'Suits', and 'Burn Notice' would be aware of the situation - and they may even discuss it, outside the scope of the invasive cameras of the Trueniverse watching them - but they would be more focused on what's happening in their home towns of Los Angeles, Boston, Chicago, New York, and Miami, respectively.
(I chose those series because they are the few that would be in operation during the events of the Chester's Mills dome.)
I just hope the network doesn't get greedy and try to extend the shelf life of the series beyond the summer. I think that 'Under The Dome' - like the glass bottle of whiskey in a certain episode of 'Columbo' - should be marked "This far, and no farther."