Just saw this (again) and thought the whole episode was amazing. The chemistry between Falk and Cash (this is where i got to like Cash's music) was fantastic to watch and i really felt sorry for Mr Brown, his wife was not a very nice person.
I also dont think that any confession would have been made, Brown would have enjoyed life too much of he had gotten away with it. More a case of Columbo suggesting a way for the court to look a bit more favourably on the case.