Okay, I got that the aliens were simply a scouting mission to see what was up with that signal they received, and we got lucky that the lost their communications ship. Shouldn't their planet eventually send another mission to see whatever happened to the first one?
Possibly not. The novelization suggests that either the Regents' leadership is horrendously incompetent, their forces are badly overstretched, or both. Their disappearance could thus be buried as a butt-covering measure or there might not be more forces readily available. Still, Earth should not count on either, and should immediately begin gearing up for round two.
So we send a signal out to the stars... and while we're waiting for a reply never once consider a bad-intentioned reply? We don't train or built one Earth-defense satellite or defense corps? Indeed the Defense secretary is surprised by the existence of this possibility despite the obviously large budget this program had?
What it boils down to is the interstellar equivalent of shouting "Is anyone there?" into a dark cave. The hope is that someone will yell back "Yes! We're here and we're friendly"...and not announce themselves by appearing in near-Earth orbit with an invasion force. It's naive to the point of painful exactly because we have no idea who is listening or what their intentions are.
We sent a signal out into space expecting to get a signal back if, and only if, life on that planet had advanced to the point that sending a signal into space was a possibility for them. It was a hopeful attempt at opening communication with another world. Interstellar travel is currently considered to be a scientific impossibility or, at the very least, way beyond our capacity to do at this time, so it's unlikely anyone expected to actually see aliens come to Earth.
We have sent plenty of signals out into space, and as far as I know we don't have sort of Earth-Defense Corps... or do we?
Out of all of the musterable resources in the entire state of Hawaii, only those three on the mountain can stop the aliens.
Only those three on the mountain know what the aliens are doing. The entire conflict is approximately one day or less in length; there's not a lot of time for intel gathering.
The scientist who was explaining the nature of ship crashed in Hong Kong hypothesised that the aliens may need the space comm station to 'call home'. Wonder why did no one offer to shut down/shoot down the relay satellite.
Hey those things are expensive, do you know how much it costs to get one of those up there, let alone build the damn thing? And then who is going to pay for all the damage to the various other satellites that'll get hit by all the debris. I'm sorry but it's just not in the budget; we're going to have rely on the slim chance that the aliens would rather enslave us rather than exterminate us.
They are able to place one call - so they call one Destroyer that they don't even know if it is in range.
Its the only thing they know that is even remotely in range. Calling the thing with the most firepower makes sense to me.
The call was a general call for any forces. They just hoped it would be the one destroyer but any destroyer would have done. That said, there is a general question of why she was hoping to reach her boyfriend, the grade-A screwup, and not her father who was in command of all regional forces (keep in mind, they have no idea what ships are in the area nor that the majority of the fleet was outside the barrier)
She wasn't "hoping" to reach her boyfriend. She was hoping to reach anybody, and was surprised when he picked up. It's not like she was asking for him by name.
Their radars are jammed, so how are they using their CIWS?
CIWS has manual overrides. As awesome as radar is, the Navy is not so foolish as to have that be the only method of fire-control. And when the John Paul Jones is trying to hit the Regent ships with pairs of missiles, they forgo radar and (in very much layman's terms) tell the missiles "fly at X angle for Y seconds/distance". Which the missiles do until they hit the water - or preferably a target.
I have no idea if the CIWS have a manual override or not, but I don't think it is possible for a person to manually hit several fast-approaching, relatively small projectiles like that.
It has an override, but they basically got lucky with its Bullet Storm. (which is more or less the selling point of the thing) The 'canisters' are thin-skinned explosives like Earth-based missiles. The CIWS was shown to hit one of the buzzing saw-balls, repeatedly, and did nothing because of their armor.
The fighters that come in at the end are able to target the canisters with missiles and then the pilots report they're locked on to the flagship before letting loose their missiles. Considering the entire plot point of how you can't target squat on these things... how?
Before any combat started, the aliens activated the shield bubble device, and only then did we see radar and other sensors go down. Once the battleship used old-school cannons to take out the shielding platforms, the cavalry was able to do its thing once again.
So...how did the aliens get onto the John Paul Jones? There's the initial attack, then we're shown the big spinning things attack the island, while the flying ship goes to the satellite dishes, then all of a sudden there's an alien running around on the John Paul Jones, and they captured one. The movie never says how they got there in the first place. Did they swim or what?