There are two error indicators:
When the power supply is insufficient the under power indication lights (occasionally) and the CPU is throttled which results in less processing power available. This may be caused by the PSU being unable to deliver required current or the cable having too high impedance, resulting in voltage drop across the cable.
xrun indicates that there is insufficient time to process a block of audio. This may be caused by insufficient CPU which may be caused by insufficient PSU current.
When an xrun occurs there will be a discontinuity in the audio signal which results in an audible click. xrun may be buffer underrun (insufficient audio data reaching the DAC) which would put hole (short silence) in the output or it may be a buffer overrun (too much data reaching DAC) which would put a discontinuity (sudden jump in sample level). The former (underrun) is most prevalent.
A weak PSU or poor quality cable is probably the most common cause if issues with Zynthian and sounds like the most likely candidate for your sound issues.