To save HD video when publishing a movie from Movie Maker, you'll need to add HD profiles to the program directory.
Depending what version of Movie Maker you are using, you may find the Profiles directory in one of the following places.
C:\Program Files\Movie Maker\Shared
C:\Program Files (x86)\Movie Maker\Shared
As the video shows, if the Profiles folder doesn't exist, you'll need to create it.
Download Windows Movie Maker HD profiles HERE.
Download Windows Movie Maker 6.0 HERE (this version has the HD profiles built in, so you don't need to install them separately!)