The worst problem, which prevents a piano from being put perfectly in tune across all "notes", is, for explanation purposes, "growling", lack of each string evoking uniform, neutral harmonics, lack of each string being supported by a bridge which is tangential, 90 degrees, able to be repaired by filing the bridge square when restringing. A tuner can only tune each "note" to a certain level of in-tune-ness, but if this "growling" is afflicting a string, it will never sound perfectly in tune, there will always be a vaguely "out-of-tune" tone. You can listen to various classical performances, to hear which...