Continuity mistake: Near the beginning of the film, "Elvis" is driving Byron's car, and has a diamond horseshoe ring on. They show a close up of it as he's driving, and in a subsequent scene, the ring has been turned around.
Continuity mistake: During the whole scene when Byron first gives Elvis a ride, and they are starting their conversation, we can see the silver tip of the transmission lever way up. So, even though they are cruising at 35 mph, the transmission never left Park.
Continuity mistake: When Byron stops the car to let Elvis drive, we first see him step off of the car. The next shot is of Elvis's reaction, but we can see Byron's hand (and his wedding ring) are still on the steering wheel.
Other mistake: When Burn and Elvis get to Memphis, Elvis says they are there for his birthday, but earlier in the movie he states he has to be in Memphis for the 16th of August, which is the anniversary of the day Elvis died. His birthday is January 8th.