Bad history and bad science = bad film
I've read a number of reviews detailing the flaws of this film, but this is one of the most interesting to me:
http://garethrees.org/2008/11/25/eddington/
It touches on three main issues:
1. The story attempts to cram too many issues into one film.
2. Too many obvious fabrications for dramatic effect.
3. The climax of the film misrepresents the facts, significantly.
This review also provides two of the actual charts and graphs produced by Eddington. I recommend reading it, because it's more informative than the film was, and the writer is clearly more talented than I am.
4. To the three criticisms in that review, I would add that there's no real evidence that Eddington was gay. Given the repeated accusation that gay historians and gay writers have to "make everyone in history gay", this is more ammunition for that (false) charge. It adds so little to the story, you have to wonder what the point was.