There are lots of things wrong about dealing with noise nuisance but unfortunately its the system we have.
there are invariably "experts" who tell you to ignore the letter, that there are times you can or cant make a noise, that if its ordinary noise from a household it cant be a nuisance but this isn't the case.
when dealing with a complaint you take into account the level of noise, the frequency, the time of day and the background noise levels. so a noise in the middle of the countryside at 11pm at night might be a stat noise nuisance but the same noise at the same time in the middle of soho might not be because the background level is so significantly higher.
of course people can lie but the person taking the complaint doesn't know this. that's why its so important to make contact once you receive the letter and explain what the situation really is.
and yes, I think if there is a noise complaint - either one you formally make about your neighbour or one that they formally make about you the sellers information forms say something like "complaints in the last 5 years". that's why I always advise people on this forum to try and resolve a complaint informally first because of this implication.
the problem with noise nuisance is that everyone wants it to fit into a neat box with noise levels and times etc but it just doesn't.
I have prosecuted people for a whole host of different noises including noise from caged birds in an aviary, barking dogs, a water fountain etc. The only one that I suppose is a bit of a sacred cow is the noise of children playing but believe me over the 20 years I worked in this field I must have dealt with 200+ complaints of the noise of children playing in the street or in the garden.