EDIT: Area updated for Pumpkin Kingdom. Credit for the find goes to BinaryHedgehog.
EDIT 2: After replaying, re-updated the Egg Argonaut information with the correct directions as well as all the stages' info in regards to what you can receive specifically.
Leaf Forest - Stage 2 = Pretty much a similar story here. Punch around up top til you find a tree you can actually punch. Destroy and the hidden area will open. Inside there'll be two NPCs being raped. Freeing the first one nets you the Red Chaos Emerald. The second one spawns a set of invulnerability pills, and for good reason since the second you get done freeing the two, you'll be swarmed by waves of Earthworm enemies.
Atlantic Ruins - Unknown.
Pumpkin Kingdom - Go down the graveyard path and beyond the grave that says "in memory of", there is a cracked tombstone. Jump behind it and head left and you'll find an orgy going on. Break it up and defeat the Demon King and Queen, which are basically really beefed-up Incubus/Succubus enemies. You'll get two halves of a key. When you reach the second floor of the ghost mansion, enter the door with the heart-shaped lock, inside is a bonus in the form of the White Chaos Emerald. For those that are curious as well, the diary in the middle of the room has a small series of amusing entries about a certain individual depicted throughout the mansion.....
> Not so much a secret I suppose, but when arriving into the Ghostess' mansion, you'll find that as you go you'll see a picture with the curtains drawn closed that says "DO NOT PUNCH THIS!" Getting past the fact that most would do just that anyway just for gits and shiggles, I would advise the more wary not to do so. You'll be satisfied you did.