I bought a house based on the realty listings, but when I went to its location in Lethensome Lift, it wasn't there - only houses for sale and none of them with my house number.
I sold it again and will try buying a house from the in-game point, but it was a bit frustrating. I didn't ever have the little mailbox appear that some people have talked about. Maybe this is a bug to do with whether you buy your house off the realty listings or in-game?