Okay, here's a short take on each story in this book, roughly ordered by how much I liked the story (best to worst).
Anxiety Is the Dizziness of Freedom
Every aspect of this story worked for me. The setup for the technology, the characters, the central question around responsibility. Caveat: the physical explanation wasn't entirely coherent, but it was easy to look past. The subject of this story reminded me very strongly of what I read 6 or so years ago on "trans-world identity", a topic that fascinated me back then. Apparently it still does today.
Exhalation
An allegory about entropy, built in such a clean and beautiful scenario that it could almost be used as educational material. This one had the perfect length for a short story too, I think.
The Merchant and the Alchemist's Gate
I really liked the writing style and the setting of this one. Also the idea of a time machine that is consistent with relativity is fascinating.
The Truth of Fact, the Truth of Feeling
Still not sure if I've figured this one out completely. It draws an intriguing parallel between how written language and digital recordings shape the meaning of human memories. It's a thought I haven't had before, that's for sure. Though I'm not convinced of the historic accuracy of the the half that is concerned with the external introduction of writing into cultures without it.
What's Expected of Us
This one basically expands on a question from "The Merchant and the Alchemist's Gate" that wasn't really relevant in the context of that story. It's really short, just 3 pages or so but very nicely condensed. The notes at the end of the collection put a spin on it that hadn't immediately occurred to me: what if there existed a physical demonstration that life was pointless?
The Lifecycle of Software Objects
I've written about this one before – bit too long, characters too bland – but the core of the story is very good nonetheless. In particular the different perspective it offers on "artificial beings" and the role nurture and human connections play in whether we see something as conscious or alive.
Omphalos
What if young earth creationism was real, and a belief in God was backed by science? A very curious "what if", because the universe it takes place in is fundamentally very different from ours. This one is more of a "look at what this would look like" kind of thing, but it makes an interesting point about faith anyway.
Dacey's Patent Automatic Nanny
Maybe I lack a decent understanding of pedagogy to properly engage with this story. It was written as a museum's informational text about a peculiar exhibit from around the turn of the 19/20th century, which was fun but didn't serve to make the story itself more interesting. I will give Chiang credit for his very convincing portrayal of the weird ideas British people back then had about raising children.
The Great Silence
Just didn't do it for me as a short story. It's mentioned in the notes that this one comes from an art installation involving other media, I think that's the main reason.