After the military fire missiles, everything outside the dome is shown to be completely destroyed, even the ground is barren. But the next day and after, every time a character looks out of the dome the outside looks normal again with no destruction, and it is not explained.
Inside a sealed dome, there would not be any significant wind, but in most shots outside, trees, people's hair, and clothing are blowing in the wind and the lake surface is choppy.
While electromagnetic radiation such as radio waves are repeatedly shown to not pass through the dome (or at least to do so with difficulty and require specialised processing in order to be detected) nobody has any trouble seeing through the dome - visible light is nothing more than electromagnetic radiation. Attempts to fire lasers through the dome also apparently fail, but lasers are just intense light pulses and should also pass through unaffected.
Although it is entirely possible to communicate with the outside world, the powers that be are never in contact with people from the outside, except for the episode where family is brought over to the dome.