In the final attempt by Alex to erase Tau's memory, he points his remote at Tau and the amount of sweat stain under his right armpit constantly changes.
When Tau enters zen mode and says "please enjoy 'Nocturne in E Minor, Opus 55,' by Frederick Chopin," what actually plays is "Nocturne in E Minor, Opus 72, No. 1" by Chopin, as credited.
Extremely unlikely that Tau, an artificial intelligence, would not know what common things are, like "trees", "whisper", "world" and "person", during his discussion with Julia.