here my test results valid for stock Nano and replacement:
1. Booting the Nano gives 1320 Hz tone out of the speaker.
2. Rotating the Encoder leads to scratching noise on the speaker.
3. Short pressing (< 3 secs) the Encoder has no impact on audio.
4. Long pressing (> 3 secs) gives 440 Hz tone for 5 secs with a delay of 3 secs.
So it would mean the rotating part of the encoder is faulty? Unfortunately I don't have a spare one on me.
73 de Urs