Nope. Why? See following point.
You are forced by law to accept all notes.
Otherwise it would break fungibility. This has been the case all over the world in various financial systems, since this famous case:
http://www.paybits.net/blog/why-fungibility-matters/
Fungibility of money can be enforced by law only in a centralized monetary system. Bitcoin isn't centralized, there is nobody enforcing fungibility by law. It's possible for everyone to define their own rules, analyse and trace everything they wish, point the fingers to coins, transactions and merchants accepting or refusing them.
Thus, in a decentralized monetary system the only way to have fungibility is through privacy. (It applies to the physical world as well: if all gold historical ownership was known to everyone - with a simple internet connection! - gold fungibility would be broken instantly. Its fungibility comes from that it doesn't convey its own history with itself).
So if I choose not to accept USD as payment that is illegal?
I'm pretty sure you can choose if you want to accept USD or not.
But from the standpoint of accepting USD but not accepting other USD that has different serial number...then I see your point.