Here are some noise and distortion measurements of the HiFiBerry Mini DAC. Without the ethernet connected, noise is practically non-existing. But also distortions look good. D2 has the highest level and higher-order noise is decreasing with each order. This is really a nice chip.
At 1kHz we see 0.0037% THD+N (distortions alone only 0.003%). However, the measurement equipment itself (an EMU0404) itself has a THD+N level of 0.002% at this frequency (in- and output together). Therefore the real noise and distortion figure might even be a bit smaller.
We also did tests at other frequencies and they look similar:
Note, that these measurements are a bit flawed, because at higher frequencies there are less harmonics within the measurement frequency range than at lower frequencies. Therefore the distortions go down. Unfortunately I was not able the extract the D2 and D3 levels alone.
There are more good news. The voltage regulation on the board works great. Even with the worst power supply I could find (a Nokia charger), the figures did not change much. THD+N went up from 0.0037% to 0.004% at 1kHz. That means there is no urgent need to upgrade the power supply of your Raspberry Pi.
Update 1.12.2013: We did some THD+N measurements of our production version. They were even lover than the values show here.