When the plane's pilots are preparing to land the second time, all three landing-gear lights show green on the instrument panel, not just the two as shown in the next close-up shot of the gear-indicators.
An underwater nuclear explosion would not cause an electromagnetic pulse (EMP). EMP occurs when the pressure wave from a high-altitude blast forces molecules in the upper atmosphere previously charged with electricity to discharge it. An underwater burst would also not produce a fireball above the surface but instead would produce an enormous cloud of water vapor.