There are a few ways to do the mirror-wrench sequence.
You only need the mirror to get the wrench from Barter, but you can also give it to Baffle to get the Sewer Stockpile clue. Whether you give it to Baffle or Barter first, you can later buy back the mirror to give to the other one.
Barter of course trades the wrench for it but Baffle has some nerve charging you ten coins for something you let him borrow in the first place. Barter is only clean and tidy when the mirror is in his possession, so I don't know what would be the definitive order to do the sequence.
I don't recall whether you can buy back the mirror from Barter if you've already done Sewer Stockpile and/or done the ending. I'm fairly sure you can't give it to Baffle at one of those points if you already have it, so it gets stuck in your inventory forever.
I'm not entirely sure, but I think there is a way to complete the entire sequence without having the mirror greyed out on the save screen like all the other items.
The only other bear-branch I remember is that Blunder's dialogue is different depending on whether you get the Krematoa clue from him or not before unlocking it.
It's a game with many secrets.