Major plot holes
First, the premise of the movie doesn't make much sense. The UN leader mentioned that the goal of the attacks was to reduce the global population to 500 million. Why would they knock out the world's power for such a goal? Wouldn't it be much more simplistic to spread some type of biological agent, or disease to which only a select group of people are inoculated against? If the goal is to significantly reduce the population, why go about it in the most inconvenient way imaginable? The premise is that the UN leaders clearly know that the armed Americans will pose a problem, so why not just kill them all through a modern method that renders their weapons useless?
Second, the final showdown just seemed utterly absurd. The family was mowing down trained soldiers left and right, but only suffered one casualty on their side. It was like watching the old GI Joe cartoon, where the GI's are just plowing through the horde of Cobra commandos, except these aren't elite mercenaries, but instead a simple, patriotic family. I mean they were supposed to be fighting against the combined efforts of the US, Russian and Chinese armies, so I don't see how they could possibly survive. Why didn't the military just send in a tank, launch a missile at their house, or drop a UAV controlled bomb on their butts like they do everyday to insurgents? There's just no realistic way this family could have survived against such military forces, and the movie failed to really flesh out the odds they would actually be up against.
Finally, it's clearly established that the doomsday weapon wiped out all technology on the planet, but everything this family has is still working properly. I get that the old man put a few vehicles in a Faraday garage, but why are the walkie talkies and radio equipment still functioning? Moreover, how do they plan to get the recording of the evil Russian guy out to the public when nobody has a working radio or other communication device?
It was a so-so action flick, but I just couldn't comprehend how they didn't address so many glaring plot holes, especially with the actual premise itself.