Seeing some of the other criticisms of Brigham and from members of the Mormon Church I'm not in a position to talk about accuracy. I've seen and reviewed several LDS films about the early church days and things like American Zion, The Work And The Glory and A House Divided which were also covering the same period of history as Brigham were better made and better production values. I don't see much different however in the subject matter and how it was treated.
I did see however a serious and sincere work that certainly could have turned out better say had it been shot at 20th Century Fox like their Brigham Young film. I did recognize some of the footage not too well integrated or colorized as part of the film.
The only actor that most outside the LDS church would know is Richard Moll who played the brain dead court officer in Night Court. He certainly had the height to play Joseph Smith who was reputed to be a tall man. So was Vincent Price who brought a certain saintly other worldliness to the role for 20th Century Fox. I'm sure Price also had better direction than Moll got here.
Joseph Grandmaison played Brigham Young as the kind of rugged guy I always conceived of him. Grandmaison seems to have limited his career to LDS features.
One has to remember that this is not a Hollywood production so a little charity is in order. Like Savage Journey the film edited from this for television it remains a kind of Mormon primer for young LDS members who can get more deeply involved in their church history with a little research and viewing those more recent films I've mentioned.
If Mormons are anything else they are good archivists. As I stated in my reviews of those other films the church obviously has a lot of archival material of people who lived through the times portrayed. This film has a good eye for the Jacksonian era it portrays.
More than LDS audiences might benefit from watching Brigham.