The first most annoying thing about the trailer was the voice of the narrator. When thinking about post-apocalyptic fallout, droning nasal banter is not something that comes to mind.
Second, all that lush environment better be full destructible. Nothing anaesthetises the feeling of immersion more than coming across a shelf, computer, or squishy whatever, that you can't blow to bits with your fat-boy tactical nuke. If I can't make a hole in a building with it, then the world is static. Fully destructible environments, IMHO, are the next holy grail of immersion. For those that played the Silent Storm series, will know of what I speak.
Third, and I really hope this doesn't apply, the world may be large but is it varied? This trailer shows a lot of drab and grey burned-out car hulks, shelves, and rubble. Sure, I expect this after the apocalypse, but let's not make it the same car hulk, the same shelf, and the same rubble around every corner.
Overall impression - meh.