The Sphinx has the ability to cut guns in half with his mind; so why didn't he use this during the raid on Casanova's castle? He has his reasons, but they're probably terribly mysterious.
Sphinx deliberately pissed off Furious with things like the watermelon prank, in order to get him in touch with his true fury, which was meant to be directed at external enemies. Previously, his true fury had been tied up by the fact that he was not who or what he wanted to be, and when it came to actually attacking anyone with it, he'd been faking most of the rage.
The moves done as Mr. Furious finally takes down Casanova Frankenstein. A finger hook, ear slap, short elbows to the chest... all seem rather weak. But they are actually great ways to hurt someone. Finger joints and bones are very weak and prone to pain. Boxing the ears like that can easily rupture the eardrums. The solar plexus (center of the torso, right below the breast bone) is a bundle of nerves and a hit there produces the feeling of "having the wind knocked out of you" by causing spasms of the diaphragm. Simple moves designed to cause maximum pain with minimum effort and with less chance of missing.
Ancient civilizations all around the world typically did not have a word for "blue", and (assuming mankind could even comprehend it yet ) simply referred to the color as "green". Somehow, the idea of a green "blue raja" doesn't seem too far off.
Why would Captain Amazing, the only serious hero in Champion City and thoroughly dedicated to his job, require a publicist? Well, it appears to be a case of avoiding the Hero with Bad Publicity trope that has come up in recent years, which is all right... except by the time of the film’s story things in town are so stagnant that Captain Amazing's reputation has degraded into vaguely good publicity without real heroism. He's a hero, but at this point he's a hero that just beats up crooks that the police could easily handle. He doesn't need a publicist to maintain his good name, he needs one to make sure that the public doesn't forget he even exists and to try convincing the corporations that he's still worth their sponsorship money.
Captain Amazing, with his sponsorship deals, has the secret identity of billionaire lawyer Lance Hunt, who acts as his representative. That would mean that Hunt gets a hefty profit from arranging deals for Amazing, which makes his desire to get better deals a lot more understandable.
It also means that the link between the two is a lot more plain, if anyone cared to act on it.
Casanova Frankenstein's I Know You Know I Know dialogue with Captain Amazing could be seen as a Secret Test of Character. Amazing fails it, not because he couldn't match his intellect, but because he didn't care. Even when Casanova reveals that he knows Amazing is Lance - which means he knows why he was released, enough of an alarm in superhero/villain tradition - Amazing just expects him to do the same thing all over again. Frankenstein is probably more than disappointed at Amazing's "happy to be stuck-in-a-rut" attitude and not even caring if things were different.
In the same scene, Frankenstein defeats Amazing with such ease that one has to wonder how Amazing ever got him thrown in the asylum in the first place. Though it was probably so easy because Frankenstein has every advantage in the situation. He's smart enough to have figured out why Amazing had him freed, so he knows that Amazing would come running to battle him in his lair as soon as he blew up the asylum. He sets things up so that the battle occurrs in a time and place of his choosing, and then lulls Amazing into a false sense of security.
Fridge Brilliance: Dennis shows remarkable arrogance when it comes to combat situations - in fact, he even wins some of them, no matter how unlikely that a Badass Normal could go toe to toe with a giant supernatural werewolf. Why is that? Simple: His mask is, unbeknownst to him, the Mask of Eternity. He's used to having fair fights, but is unaware that he's cheating in all of them.
) simply referred to the color as "green". Somehow, the idea of a green "blue raja" doesn't seem too far off.