I just watched this, and I loved it, despite a boatload of flaws. Even at 3 hours on TV, it really didn't cover all of her life. Shirley does a nice job with the few minutes she is given, but kudos really belong to Barbora Bobulova, the young Coco.
Here is one very on-target review. The criticisms are all fair, IMO, although the reviewer clearly didn't enjoy it as much as I did. I agree - history definitely took a back seat to feeling. Note that fashion is defined by selected chunks of Coco's sense, dragged out at various points to show her drive. I thought that perfume fans were truly slighted by the script. If the movie shows all that Chanel did for no.5, then her name should be taken off the stuff. They should have given it at least a little more time.
There is good coverage of the movie and Chanel herself on Wikipedia. It sounds like this flick got the facts right. And it sounds like more movies are coming, including one with Demi Moore. Let's hope that one does more to serve the perfumaniacs!