During one scene set in Dick James's office in the late 1960s, Elton sings the first bar of 'Sad Songs (say so much)' only to be met with James's remark "Too depressing". This song was not actually written by Bernie Taupin until 1983 (and released in 1984). At the same meeting he also sings a portion of 'I Guess That's Why They Call It The Blues' (written in 1982 by Taupin and released in 1983). Whilst these are technically anachronisms, the filmmakers have also said this film is not a factually correct biography and that they took some liberties for the sake of the story.
Elton and Bernie are driven to their gig at the Troubadour - which occurred on 25 August 1970 - in a 1977-1979 Lincoln Continental (identifiable by the tall chrome front grille). As they arrive at the Troubadour, they are passed in the other direction by a dark-colored late-1980's Chevrolet Caprice (identifiable by its flat, flush taillights).
When Elton & Bernie first go to the US in the early seventies, there is an aerial shot of the Hollywood sign. The radio mast adjacent to the sign has modern telecommunications transmitters/ receivers on it that were not developed in the 1970s.
John - in Elton John - here attributed to John Lennon, rather than Long John Baldry. Most likely not a real goof given it enabled the film to give a little nod to John Lennon, a close friend of Elton's way back when. There would likely have been a lot of additional leg work needed to work Long John Baldry into the narrative, whereas John Lennon needed little more than a photo.
When young Reggie first enters the Royal Academy and meets his piano playing to be tutor, she greets him with her hand held out (to shake) and asks how is he, to which the young (c. 12!) Reggie replies (just): "Good"! No young British working class - even if 'upper' so (from Harrow?) - boy of the fifties / sixties would ever greet an adult, let alone one who was his to be his tutor in a prestigious new position, with such a (modern, U.S. style) lame, even disrespectful way.
While the film implies that Elton John went to rehab outside of New York City (he storms out of Madison Square Garden and the NYC skyline is visible in the background as he arrives at the treatment center), he was actually treated at Parkside Lutheran Hospital in Chicago, which he has claimed was the only facility able to treat his multiple addictions simultaneously.
Near the end of the film, it is implied that the song and music video for, "I'm Still Standing" depicts Elton celebrating having finally become sober and conquering his addictions. But he did not give up alcohol until after filming the music video; in fact, Andy Taylor of Duran Duran recalled getting drunk with Elton on martinis in Cannes during filming, and throwing a massive all-night party in which Elton's personal assistant's hotel suite was, "leveled." Waking up the next morning, a hungover Elton surveyed the damage and asked, "What happened?" The assistant replied, "You happened!," and Elton gave up alcohol shortly afterwards.