I'm going off of memory, so some of this may be out of order/not quite right.

Pick up the board and cheese. Use the board to move the crate. Open the trap door and throw the cheese to the rat.

Go downstairs. Pick up the salt and use it on the vat of vitriol.

Go back upstairs and pick up the empty bottle.

Go downstairs and fill the bottle with the hydrochloric acid.

Take the cork from the table and combine it with the bottle of acid.

Go upstairs and use the acid on the lock.

Take the wrench and go downstairs again. Use the wrench on the large distillery thing (can't remember the name) to get a metal pipe.

Take the wire from the distillery equipment and combine it with the metal pipe in inventory.

Go upstairs and use the combined pipe/wire thing on the door.

Take the picture from the shelf and leave the hut.

I seemed to have just the right amount of inventory slots left to accomplish this. So if you started the chapter with more inventory slots filled than I did, this might not work for you.

• Can you do anything with the safe in the manager's office?
  
• How do you get tools from the toolbox (the one that's outside, not the one that's inside by the stairs)?
  
• When you stand next to Katie's bed the gears symbol appears. However, all she does is talk about how tired she is. Can I do anything else here?
  
• How do you get to the area behind the hotel (where the dock is, not where the patio is)? I'm convinced that this must be possible because I saw a screenshot with the main character in that area during the day (not during night time, which happens later in the game). Here's a link to the image I'm talking about.

You don't actually go inside the jail, but you do help the janitor escape. There's a grate in the ground near the jail door. Once you're standing next to it, you'll be able to talk to the janitor and he'll tell you what he needs.