I haven't seen any of the TV series but it's on my "to watch" list. I'm not particularly bothered by spoilers so I had a quick look at your pdf.
Presentation is great
although you might want to check your spell-checker
In the section for Stun Gun Effects there is the word Agiliyu, I figure you probably meant Agility but your keyboard was refusing to play nice
- me, I got fat fingers that can't work on a keyboard properly... that's my excuse and I'm sticking to it!
I haven't got any basis for commenting on the game stats because, as mentioned, I haven't seen the show yet but in general, the game mechanics/rules look fine.
As an aside, have you considered submitting this background to any fanzines? I think you could submit it to Protodimension ezine for example (although it would have to be in a non-pdf form so they can format it for the ezine).
Although the magazine is devoted to conspiracy horror RPGs, I think Falling Skies fits in alongside Dark Conspiracy, Delta Green, Conspiracy X and the like.
Their submission page can be found here
http://www.protodimension.com/zine/submissions.html