I ran around randomly. I mostly tried to explore the clockworks where you start Chapter 3, because I remember thinking "HEY, I WANNA GO THERE," and went from there. I tried heading for a bell, but when I discovered there was a door charge I started going in a semi-spiral pattern.
I've been doing a few experiments in the Disorder. I do not know if there's anything in there that you can't find outside - that is to say, if there's items to be found there or events to be had other than "make it in" and "make it out". I'm getting okay at the Disorder, and can more or less orient myself correctly. I have a habit of overshooting.
To finish the game, the disorder is just a fast travel meganism, and you don't even need it to complete the game. However, if you have finished it, the disorder is one of the places where you can find some secrets. And I do say one of the places. ;)
I've been a little reckless with my trading, actually. There are some valuable items that I could have kept, rather than receiving a simple "thank you," or a junk item. Hopefully those didn't screw me over :P
I was hoping I could give my golden bird to the alchemist, but ended up accidentally trading it for what looks like some pipes taped to a glove. Does anyone know if the alchemist... wants a golden bird? :3
Just kidding. You couldn't have traded the bird statue with the alchemist even if you kept it. The only use of that object was to trade it for what you got. Some of the NPCs are real jerks in this game! XD