Depends on your headphones, I guess. The N8 probably has exactly the same hardware as the C7 in this regard so my experience with the N8 should be relevant.
I absolutely notice some very faint hiss and, worse still, a quiet periodic ticking in my Westone UM1 IEMs when I am listening on my N8, but only when the screen is on or when it's charging. It's also pretty low amplitude - will be drowned out by music but it's clearly audible in quiet or silent music segments. When the screen is off and the phone is not charging, then the sound quality is wonderful. Perhaps the best music experience any Nokia phone has ever delivered.
If you don't have sensitive in-ear monitors, then I doubt you will notice anything at all and it will sound great to you all the time. I also didn't notice anything abnormal in a pair of Grado SR80i on-ear open headphones. It's likely just really sensitive in ear monitors that are going to pick this up.
Coincidentally, I also had an E71 and it was totally unusable with the Westone headphones. The N8 is a million-fold improvement over the E71 but it's definitely not perfect.