Well, okay. Here I go again . . . defending the 1971 film, tho' I (along with many others) have done so at various other locations on this site. In terms of a great, lasting cinema experience, i.e. Citizen Kane? No. In terms of epic sweep? Yes. Not as cohesive, say, as Lawrence of Arabia--three plot lines alternate, and for many people (including some critics) these three plot lines are disconcerting--but overall I think of it as a film that is intriguing and sumptuous and haunting enough to have brought many of us to Robert Massie's book, encouraged us to take classes in Russian history, and eventually led us to this website.
As for the animated cartoon, Anastasia? It starts out promisingly enough, and in some ways dovetails with the 1956 Anastasia. But eventually--for my tastes--it becomes just one more showcase for a crazy uber-villain, i.e. you-know-who. Much of the artwork is beautifully executed, the voice characterizations are generally well-acted, and I really wouldn't have too many problems with a child seeing the cartoon, as long as he or she is told that most of it is fantasy, in particular the nightmarish conception of Rasputin.
Vigilant parents who prescreen whatever their children eventually see are at least part of the answer. I remember reading that Jacqueline Kennedy made a point out of seeing Anne of the Thousand Days first, before bringing her pre-teen daughter Caroline. Thereafter my respect for her increased one-hundred fold.
As for the 1971 film, I find many more merits than demerits. The HBO film re: Rasputin? Well-produced and intriguing, although I prefer Michael Jayston and Janet Suzman as Nicholas and Alexandra since they are closer to what we see in the sepia photos in terms of physicality and age. (Yes, I do appreciate attempts at authenticity!) And I also must disagree with a few of the previous posters re: specific characterizatons. I felt that the character of Alexandra was well-written and mirrored very much what we learned about her in Massie's book and other books . . . and Yurovsky, though certainly older in the film compared to the real-life person, is written to show the perfidy, confusion, and ultimately hard-line attitude of those who were in charge.
Finally, I think we all need to remember that these are d-r-a-m-a-t-i-z-a-t-i-o-n-s, i.e., representations. I, too, feel that facts should be adhered to as much as possible. But just as there is a difference between fiction and nonfiction, so there is in comparing a stage play or film to a documentary. After reading Massie's book, then most of the books he lists in his bibliography, then as many additional books as possible published on the subject, I think the many people behind the 1971 film came very, very close to replicating the tone, mood, and dramatic sweep of the times.