It is part of the College of Humanities and Social Science at the University of Edinburgh. It merged with the University in the late 1990s/early 2000s. Edinburgh is a highly regarded university. I know a couple of people who trained to be teachers there more than 15 years ago, who speak highly of it, but that is the limit of my knowledge of Moray House.
I do know that the Scottish Government has cutting funding for teacher training places (see
http://news.bbc.co.uk/1/hi/scotland/8504946.stm), so I suspect that no School of Education is in great shape in Scotland.
