We don't actually know if the explosions are nuclear, do we? Can't a large enough conventional bomb raise up a mushroom cloud? I guess the dead birds at the end signify radiation though.
Any conventional explosive big enough to make an over-the-horizon visible mushroom cloud, with that much ancilary light would be way to large to hide.
The MOAB size bombs, and some conventional explosives tests can make some pretty big mushroom clouds, but you won't get the flash and glow that lasts that long, only a nuke makes enough heat for that.
Actualy, at a couple hundred miles, you probably wouldn't be able to see the nukes except for a "heat lightning effect" of light scattering in the sky either, but they had to give the audience
something for dramatic effect. And if it was terrorists, they'd just be kiloton nukes, probably not much more than 10-100kt tops, not multi-megaton H-bombs, because concealability and transportability becomes an issue.
The total loss of communications implies a widespread EMP, not just failure of local services. What about satellite TV or the internet? Why would cell phones and land lines fail, yet cars and generators still work? Either there is a bit of EMP handwaving or something more insidious is going on (combined hacker attack with NBC attacks).
EMP effects are somewhat overstated in popular fiction. Anything several hundred miles from a blast, and not hooked into long pieces of metal like land-lines, antennas, or fences stands a better chance of surviving than commonly thought. So cars and handheld electronics could well work fine, while interconnected services fail. Also, things like TV's may well still "turn on" but the more delicate functions like tuning, or IC's that control the settings could be fried. Surge strips, UPS's, and lightning arrestors can help plugged in electronics survive too. Also, a groundburst can't throw EMP as far as an airburst can. Presumably a large terrorist nuclear plot would be less likely to have the means of air-delivery...
If a dedicated EMP blast was set off several hundred miles over the earth, that would be worse, as there's no horizon to cut down on the EMP, and the EMP can be magnified by interacting with the ionosphere and Earth's magnetic field. (As they found out during that infamous Navy nuclear test near Hawaii in the Pacific...) but that takes either a secret satellite nuke, or a ballistic missile, and is still mostly the realm of somethign a first-world power, the US, Russia, Israel, India, or China could pull off.
Actualy though, the power probably would have gone out sooner, as the EMP would have overloaded breakers across the grid and created a cascade failure like the infamous northeast/NYC/Canadian blackouts. The miles and miles of power lines would have collected a pretty massive EMP surge.
Although I think they got it at least somewhat right, when the ex-cop "wise man" ("Are you sure you aren't the science teacher") suggested that it was a cascade failure from all the missing demand from destroyed cities, and that remote power plants could still be intact...
They didn't seem to be able to raise anyone on he Hamm radio, highly unlikely that after a major attack. More likely would be that you couldn't get a word in edgewise due to all the radio traffic.
While they got the HAM from the "kook", I'm not sure that they tried it yet... Can anyone remember?