I wasn't really interested to watch it, but my wife Dvr'd it and asked if I wanted to try it out.
Overall, I give it a C+. There are some problems I have with it, but it was good to see some of what they might try to do.
Spoilers ahead.
I really didn't like the lead character, the girl, Charlotte/Charlie. She's full of rebellion and angst, but it seems out of place. Her dad was portrayed as a good dad, and I don't see why she would develop the personality the story gives her.
The emphasis on "family" seems forced, and the writers know it. They wrote the uncle as being out-of-touch with family ties, and not caring that his only niece was on some mission. But yet we're supposed to believe that Charlie has this idea that loose blood lines are the ultimate tie to other people.
The notion that "the whole world is dangerous" was similarly forced.
The "event" was set up to be an EMP type thing, but for some reason internal combustion engines don't work anymore. That'd be fine if that were consistent, but then we see muzzle-loaders that work on the same fire/explosive/pressure reaction that engines work on. The science of one can't work without the science of the other, so whatever "explanation" there is for the driving premise of the show in inconsistent and flawed. But knowing JJ Abrams, there won't ever be an explanation. It will just be "things that we show working work for some magical reason, and things that we show that don't work don't work for some magical reason." This was hinted at in the nerd's questioning of the "students" as to why physics didn't work anymore. There won't be an intellectual answer given, but they will string it along as something that can be "found out."
And as others said, the whole "the govt failed so there was a power vacuum so there were violent gangs ruling the whole country/world" was really disturbing. There's no reason that the govt would fall, and there's no reason why peaceful solutions wouldn't be found anywhere except that these things were necessary for the plot.
The things I liked were seeing some action sequences that weren't just car chases and gun fights. Swordplay on network TV was interesting to watch, even if the outcome was entirely predictable. Some of the characters were well played, despite the stilted roles written for them.
I'll keep watching for a while to see where it goes, but it's not a show I'll be upset if I miss or it get cancelled.