It means that the neighborhood (in terms of quality) is decreasing greatly.
For example,if you see freshly cut grass on the parks suddenly dying and having a poorly maintained look and littered with garbage. And if you see things like Graffiti on the walls or trash everywhere,etc.
HOWEVER,it actually has very.....racial origins. Basically,it was shown as disapproval and disgust when a minority moved into predominately white neighborhoods.
This link basically explains it better with more elaboration(while still being understandable and to the point):
http://english.stackexchange.com/questions/59672/what-is-the-origin-of-the-phrase-there-goes-the-neighborhood-and-does-it-have
There Goes the Neighborhood - 2009 Freedom 1-6 was released on: USA: 13 September 2009
The A-Team - 1983 There Goes the Neighborhood 4-10 was released on: USA: 3 December 1985 Netherlands: 3 February 1986
Being Human - 2011 There Goes the Neighborhood Part 1 1-1 is rated/received certificates of: USA:TV-14
the word agrestic means rural and the neighborhood is called agrestic so a rural neighborhood.
Mr. Box Office - 2012 There Goes the Neighborhood - 1.24 was released on: USA: 5 July 2013
There Goes the Neighborhood - book - was created in 2006.
There Goes the Neighborhood - book - has 226 pages.
There Goes the Neighborhood - TV series - was created in 2009.
The duration of There Goes the Neighborhood - TV series - is 3600.0 seconds.
There Goes the Neighborhood - TV series - ended on 2009-09-13.
There Goes the Neighborhood - Sheryl Crow song - was created in 1999.
Driven by Vision - 2009 There Goes the Neighborhood was released on: USA: 3 February 2009
There Goes the Neighborhood - 2009 Freedom 1-6 was released on: USA: 13 September 2009
Backyard Wrestling 2 There Goes the Neighborhood - 2004 VG is rated/received certificates of: USA:M
When Things Were Rotten - 1975 There Goes the Neighborhood 1-8 was released on: USA: 29 October 1975
Arnie - 1970 Well There Goes the Neighborhood 2-2 was released on: USA: 20 September 1971
There Goes the Neighborhood - 2009 Box Lunch 1-5 was released on: USA: 6 September 2009