Just saw this the other day, and found it very enjoyable indeed. "Marvelous" at times.
Anyway this is one of those films featuring known people that you actually can "meet" that person. No small effort afforded by by Michelle Williams, who was a rather surprising choice for me prior to the viewing of the film, but then equally surprised that she pulled it off with ease. The story follows her UK trip which resulted her been starring in the film called "The Prince and the Showgirl, with Sir Laurence Olivier opposite of her and behind the camera[directing]. He was portrayed by Kenneth Branagh, what's interesting about that, that he was compared to Olivier when he started out along with his then wife Emma Thompson to Vivian Leigh . Branagh really nailed Olivier as one could guess, and there was a host of fairly well known British actors appeared alongside as well. The film is rather sympathetic to the Monroe character,which basically is filmed from the POV of the young English guy who was a "gofer" of the crew, but became a bit more then that as the film progresses. It was his diary that the film was based upon. It creates enough depth to learn why she is the way she behaves instead of just portraying her as a diva with a severe case of stage freight, which wouldn't make a very pleasant experience for sure. BTW Williams performs the songs in the film that originally performed by Monroe, and the "Marilyn theme" by Alexandre Desplat is very moving. I saw this on BD and it is flawless for picture and sound.