One more thing, I've noticed some slight buzzing / distortion in the right ear for some parts of some songs. After investigation I have found it occurs for frequencies between 445 - 465 Hz, being most pronounced in the middle of said range.
Is this a common issue? Is this something I can fix by tightening something or would this require a call to Hifiman to see if I can get a warranty replacement?
That doesn't sound normal at all. If the connections are tight on the headphones I would give them a call tomorrow.