I think people are so hellbent on clinging to the characters from the past series that it's gotten to a point where the mere idea of any new main character from The Legend of Korra being their "own" character that doesn't have some sort of super secret special ties to a character from the previous show goes way over their heads. Ex. Mako has to be related to Zuko, this character must be Aang's illegitimate kid, Tenzin and Lin Bei Fong had a lovechild that turned out to be this character, Amon is probably Azula's son, or some other insane theory about how every new character that's introduced has to have some sort of hidden clandestine ties with a preexisting character from the old series.
We already know The Legend of Korra is going to have some ties to the old series, and there will be some future episodes that will feature characters that had ties to past characters (such as an upcoming episode titled "Skeleton in the Closet.") But at the same time, to just assume every new character from Korra or every yet-to-be-introduced character is somehow a secret lovebaby/family member/sister/brother/lover/whatever-relation to a past character just seems not only unimaginative (like fanfiction-level unimaginative) but also like it's not giving the creators behind the show enough credit. Like they don't have enough imagination beyond, "hey let's just make every major character from this new series somehow related in a weird, bizarro and clandestine way to all the old characters (even the minor ones) from the previous series."
I think when it gets to the point where people are insisting that major characters and villains are somehow heavily related with even minor characters from the previous series that never appeared for more than one or two episodes, I think it just descends into realms of complete silliness.
Sure, there will be characters with ties to the old cast, without a doubt, but Aang and a number of them have passed on and it's been over seventy years in the Avatar universe. Sometimes new characters are simply that -new characters. Sometimes Mako is just Mako, Bolin is just Bolin, Asami is just Asami, and Amon is just Amon.
I admit that I didn't watch all the episodes from the old series, but at the same time I feel like Korra is something you can get into without having to having to had watched all of Avatar: The Last Airbender, which is part of why I think all the overabundance of character-relation/twist conspiracy theories are somewhat silly.


That being said, in regards to episode 3/the Revelation:
-Despite the insistencies of many people, I don't think Amon is Bumi (Aang's oldest son). In the episode, you can get better closeups of Amon's hands/eyes and their skin color isn't even remotely the same.
-I'm not even going to go into how ridiculous/unfunny/beaten to death the Cabbage Man theory is by this point.
-I'm not really that big on the "Koh the Face Stealer" theory either. I think spirits and the spirit world may become a part of the series later, but just as I said with the convoluted character relations theories, I think just saying spirits are behind it is simply isn't giving the creators enough credit. Amon may or may not have dealings with "spirits" or the spirit world, but at three measley episodes, it is simply too early to tell and he could just as easily be lying about the spirits "speaking" to him as he is with his backstory (also, under his mask you can see he has eyes and skin, so I really don't believe his face was stolen either).
-I think Amon is lying about his backstory with the childhood farm and a firebender killing his parents. I have a feeling something did happen in his past to influence the way he sees Benders, but a part of me feels like he made up that backstory to gain sympathy/cause from potential Equalist sympathizers and with further excuse to keep his face hidden. His face may not even be burned at all (there's also the possibility that the same guy who mugged Mako and Bolin's parents was the same firebender who killed Amon's, if the story was true, but right now I think there's a sleazy undertone to Amon's sobstory reasoning and there are plenty of benders from all sides who can be criminals, so it could be two separate firebenders in two separate acts entirely).
-Setting that aside, Amon seems to be a promising villain thus far and I'm hoping he continues to deliver even after he's been unmasked.