I don't think you can really fault the movie for historical accuracy. There's some cinematic heightening and dramatic shorthand, but the events and major players are all faithfully recreated.

I'd say problem is primarily in the tight focus on Oppenheimer's love life in act 1 and the entirely underserved treatment of his fight for security clearance in act 3.

Inaccuracy isn't really a part of it. It's more kind they spent 10 minutes filming Cillian Murphy make a sandwich.