The humorous British-English phrase you can hear the neighbours change their minds and its variants are used when the dividing walls between adjacent houses or flats are thin.
The earliest occurrence that I have found, about newly-built houses, is from the Leamington Spa Courier and Warwickshire Standard (Leamington, Warwickshire, England) of Friday 17th September 1909:
MR. POINTER, M.P., AT WARWICK.
Under the auspices of the Warwick Socialist Party, Mr. Joe Pointer, Labour M.P. for the Attercliffe Division of Sheffield, spoke in the Market Place, Warwick, to a large gathering on Friday night. […]
Mr. Pointer, who was given a very patient hearing, spoke at some length. […] He did not know the local conditions of Warwick. He could not say whether they had any slums. They in Sheffield had both new and old slums. He did not know whether they knew the difference between new and old slums. New slums were being created in the main by the high price of land. This is how it was. The jerry builder comes along, finds a suitable site, and has to pay in eight—he would not say nine—cases out of ten an enormous price for it. The builder, not being a millionaire, either has to crush a lot of houses together or make the walls so thin that you can hear your neighbour change his mind. (Laughter.)
The second-earliest occurrence that I have found, also about newly-built houses, is from The Evening News and Southern Daily Mail (Portsmouth, Hampshire, England) of Monday 26th April 1920:
Mr. George Hicks (President of the National Federation of Building Trade Operatives), referring to the Government building scheme on Saturday, maintained that in some places the houses would eventually become slums, as they were built too close together. The dividing wall between each of these houses was so thin that one could almost hear one’s neighbour change his mind.
According to the account of a speech that he delivered at the Congregational Church, Bexhill, published in the Bexhill-on-Sea Observer (Bexhill, Sussex, England) of Saturday 22nd September 1923, the Rev. William C. Poole used the phrase of the dividing walls between adjacent flats:
The world suffered from geographical shrinkage. By that he did not mean the world had got smaller, but that it was possible to move on it far more quickly than of old. Jules Verne’s book, “Round the world in 80 days” was written at a time when to do that was a great feat, but before he was 35 he (Dr. Poole) had got round the world over practically the same course in 38 days, and there were no “airplanes” then. Now, using “airplanes” the traveller could make Jules Verne’s record sound like a nursery rhyme. One could walk in New York one day and in London the next. They were thus living in a shrunken world. It was as easy and almost as quick to hear in New York what had been said in Parliament in London as it was to hear people talk in the next room in his boarding-house in London, where the partitions were so thin he could hear his neighbours change their minds.
The phrase was used of the passage of sound between floors in an article about “the conversion of large London mansions into flats”, published in The Honolulu Advertiser (Honolulu, Hawaii) of Sunday 26th December 1926—itself quoting The Times (London, England):
“Unfortunately, there is one respect in which even the most expensive and specially designed flats are seldom satisfactory; they are not self-contained as regards what is commonly called ‘sound proof.’ The ordinary house is still efficient in that point, and the saying is ‘You can almost hear them change their minds on the next floor.’”
The phrase does not seem to have been frequently used in American English; however, I have found this tongue-in-cheek advertisement in the Los Angeles Times (Los Angeles, California) of Sunday 28th April 1963:
3 TINY bdrms. + fam. rm. on cramped lot in neighborhood overrun with children. Neighbors so close you can hear them change their minds. Ridiculously overpriced. For laughs see it Sat. or Sun. at 2849 Westbrook Ave. (Nr. Nichols Canyon Rd. & Woodrow Wilson Dr.) Or call CR. 1-8579