The dark trio are able to successfully power up the Eclipse Cannon with six chaos emeralds to blast away about 1/3 of the moon. Why does Eggman want more?? What could they possibly gain by "destroying an entire planet"? And none of this explains why Eggman and co. later decide to save the world.
I can answer at least one of these. The first part has always bugged me, too. However, regarding the second question: Eggman's original goal was to point the Eclipse Cannon at the world and extort whatever he wanted, on pain of "Make me your supreme ruler or I blow you all to Kingdom Come." Seeing the world actually be destroyed (and at no benefit to him) was another matter altogether.
Plus, how was anyone to guess he wouldn't actually go through with destroying the world? He is pretty crazy.
With only 6, he was limited to striking at a single country at a time, leaving the others free to gang up and attack, forcing a single country to make a Heroic Sacrifice.
The world didn't know that though. He was essentially bluffing the world into surrendering anyway even if he couldn't secure the last emerald.
Yes, but as they said, the cannon was taking too long to charge up (after they fired the warning shot) without the last emerald. Even if the cannon was charged, Eggman would still probably want the last emerald, even if the only reason was so it wouldn't be used against him.
Eggman is crazy, yes, but not stupid. He knows full well that if he destroys the planet, there won't be anything left for him to rule, and he actually says almost exactly this in Sonic Unleashed, to the point where he's happy (well, not exactly happy, but willing if a little reluctant) to work together with Sonic if something else is actually trying to destroy the world. He was never intended to fire the Eclipse Cannon at the planet, he was just using it as a threat to put the fear of God into the people on the planet.
In Sonic Adventure 1, Sonic and his friends saved Station Square and probably the world by stopping Perfect Chaos, but in Sonic Adventure 2, he is chased after by thousands of cops and army men for something that somebody that looked a bit like him did, without him even getting a chance to explain what was going on.
They knew it was Shadow, but didn't want that secret out, so they used Sonic as a scapegoat.
Actually, that's a pretty good answer. G.U.N. probably did know that their BiologicalDoomsday Weapon escaped and had stolen a Cosmic Keystone, but they didn't want that getting out otherwise it would create a panic. So they arrested Sonic, not so they could say that they captured the bad guy, but they may have very well have been trying to recruit him into stopping Shadow for them. Of course Sonic escapes, and they can't just have him running around while the public thinks he's a villain, so...
Actually, it gets even better the more you think about it. G.U.N already had a spy in Eggman's midst, who just so happened to have a Chaos Emerald that he was looking for. But of course she then proceeds to direct him to three more of them, and where are they...? Only a place that is both 1. at a G.U.N owned fortress and 2. The exact location of Sonic the Hedgehog (who is there because G.U.N put him there). G.U.N had what Eggman wanted, and through Rouge were essentially were able to predetermine the battlefield, making the Prison Island incident a massive-scale yet subtle sting operation that simply went horribly, horribly wrong. Nevertheless, G.U.N had a lot of influence and knowlege of the game's events (spying, media control, being responsible for key events), it's easy to forget that when aside from their robot forces, they remain very much behind the scenes. There's a great deal of suspicious occurings in the game that can be explained via their involvement... Because chances are, it benifiets in some way to them.
Another theory for why the general public might believe it: if Sonic the Hedgehog were to turn to the dark side, perhaps changing his colors would represent this and his blue hue is just a mask. In the game world, there doesn't seem to be too many hedgehogs, so it would be relatively easy to jump to this conclusion.
How did Gerald Robotnik reprogram the ARK, Eclipse Canon, and the Biolizard from his jail cell on Prison Island?
Since when is Knuckles the world's greatest treasure hunter?
That was obviously Sonic sweet-talking Knuckles into hunting for keys, but if you want to take it at face value...Knuckles IS probably one of the greatest treasure hunters in the world. He's always been able to get his hands on precious jewels, his exploratory skills and abilities allows him to travel to places that other hunters could only DREAM of, such as the Gigan Rocks, the depths of the Lost World of the echidnas and even into the depths of space! It's been implied since the Classic era that he's been an avid treasure hunter, Fang was MIA, and the Babylon Rogues didn't exist at that point. Aside from Rouge, whom he ended up getting the upper hand against in the end, Knuckles was probably the only hunter who could do the things he did.