So, I happened to walk in to a tree... and I mean actually in to the tree... and discovered a "secret room". There's nothing there, and you can't actually walk in to the room, but I found it interesting nonetheless.

The is another secret in that first room, which is what walking through the tree is supposed to lead to. It's a nice tribute to another game if you find it. ;-)

There's a whole lot of such secrets in the game. Most, though, are only discoverable with the final upgrade, after the conclusion of the story.