I Have a problem with how quickly new policy was set here
and I disagree with the decision made in this instance
(badp suggested that if I have a problem with it, I should post it in this thread, so I'm hijacking my own answer to say it)
hidden (adjective) 1. : being out of sight or not readily apparent : concealed
This is the definition we appear to be operating on in this context.
Now, what appears to matter more is the word it is describing.
Hidden areas are the easiest to define, because most games have a specific progression that you must follow and possibly some obvious optional areas. Hidden areas would be concealed areas that you aren't required to complete the game in a normal manner.
Yes, this does mean some games have more hidden areas than others. Castlevania: Symphony of the Night has the entire second half of the game as a hidden area; you won't encounter it if you head straight to the throne room as soon as possible.
Hidden mysteries is actually referring to easter eggs.
easter egg (noun) 2: a hidden feature in a commercially released product (as software or a DVD)
This definition rolls it into the next term, hidden features.
Easter Eggs are usually something hidden in a hard to reach spot, quite often a reference to something outside of the game you're playing. Thus, your example on The Bridge of the Pyro's Hadouken taunt wouldn't count, because it's extremely easy to find.
Easter Eggs aren't the only type of hidden feature. There may be hidden game modes that you can only enter by entering certain codes that are not mentioned anywhere in the game. The strangest I've encountered of this type was on the Making of Lunar: Silver Star Story Complete Disc for the PS1. If you entered a code during the video, it would load a remake of the game Warlords.
Again, hidden is the operative word here. Some games may have multiple endings that are determined by specific decisions you make during the game. These aren't hidden, because they are explicitly determined by you.
Hidden Endings are things like the UFO Ending in Silent Hill, where you must take a very specific set of actions hinted at nowhere in the game to get them.
Chrono Trigger is another game with a lot of Hidden Endings, because they are only accessible if you start a New Game+, then hop directly to the final boss battle at specific points in your second playthrough. These endings aren't canon and include a number of funny things; in one, Reptites have taken over the world and everyone assumes you're disguised as humans, who died out millions of years before.
Cave Story has a hidden ending unlocked by failing to rescue someone at a specific point in the game, then performing specific actions at various points in the game afterward.
What do we do with these questions?
Easter Eggs and Hidden Areas have fairly concrete definitions. Hidden Features is a bit iffier, although if you ignore things that are unlocked as you progress through the game, it's not as bad. Hidden endings are OK as long as you note that they involve decisions that are not done through a normal course of the game, and likely aren't intuitive at all.