In the studio, right before a 1969 concert, the Doors' manager tells Jim "I am not going to go through this again with you, and lose you at the bottom of a bottle of Southern Comfort like Janis [Joplin]." The next scene takes place in spring 1970. Janis Joplin died October 4th, 1970.
Backstage during The Ed Sullivan Show, the band watches the infamous 12th Street Riots in Detroit unfold on TV. The riots took place July 23-28, 1967, and the band appeared on the show on September 17th, 1967.
At the Miami concert, Jim Morrison has a boom stand for his microphone. After a cut to an audience shot, the camera goes back to Morrison, with no microphone stand. After another audience shot, the camera returns to Morisson, and the microphone stand is back.
In the film, the New Haven concert is a sold-out show, in a beautiful theater with a balcony. In real life, the show was at the New Haven Arena, a broken-down hockey rink with no balcony. It was also half-empty.
In the film, a female photographer sexily encourages Morrison to take his shirt off, resulting in the iconic "Young Lion" photo first seen in the Village Voice, and later used as the cover photo for the Doors 1985 "Best Of" album. The photographer was actually a man, Joel Brodsky.
As with most biopics, some of the events did not occur exactly as they are portrayed in the film, or may have happened at a different time. Some did not take place at all and are included purely for dramatic purposes.
Morrison says "Well we're a sullen group, Ed" without moving his lips. This was done deliberately to allow the audience into Jim Morrison's thoughts for just a moment. He could not say "Well, we're a sullen group, Ed!" directly to Ed Sullivan without being thrown out immediately. Instead, we are allowed to hear him think it, which leads us to the mischief Morrison got up to live on air.
Another example of deliberate audio/visual mismatch is when Jim is approached by a groupie at Andy Warhol's party. Replying to "Hey Jim, remember San Francisco?", Jim says "Uh no, not really", without moving his lips. We are allowed to hear him think in his drug addled state.
During the Magazine photo shoot, Jim begins to wander around the studio with the photographer following him, still taking pictures. A flash continues to go off, yet there is no flash on the camera, they are still on the stands on the set.