I'm not sure whether this film is intended as a biopic or a Baz Luhrmann extravaganza. As a biopic, it has a lot of weaknesses. As an extravaganza, it's five stars all the way.
Whether you're an Elvis fan or not (and personally I'm ambivalent), Austin Butler is the best reason to see this film. He gives an extraordinary performance.
My criticisms are as follows: The film doesn't always offer a coherent narrative and towards the end it frays and fragments. The script, especially in respect of supporting characters, leaves a lot to be desired, leaving people who were important in Elvis's life drawn without flesh and bones and good actors left with nothing to work with. A lot of detail that might negatively affect people's view of Elvis's character has been left out, making the whole thing smell faintly hagiographic. Col. Parker is cast as a cartoon villain although I suppose the way he is represented leaves room to insert some social criticism about the frequent and inevitable car crashes we often see at the intersection of art and capitalism. And last but not least, Tom Hanks' make up reminded me of Eddie Murphy in the Nutty Professor (not a good memory).
But in spite of all that (and maybe even in part because of it), the film is fabulously entertaining. I would watch Austin Butler out-Elvis Elvis again.