John Denver's father died in 1982. The song they were playing just before he's told that his dad had a heart attack was written after the Challenger disaster in 1986.
Depicted playing "Take Me Home, Country Roads" on stage in 1972, Denver's backup band has an electric bass. In the 1970s however, Denver always toured and recorded with a double bass.
In the backstage scene after the 1972 performance of 'Take Me Home, Country Roads', a fan can be seen holding an LP of the album 'John Denver's Greatest Hits Vol. 2'. This album did not come out until 5 years later, however, in 1977.
Rocky Mountain High was written on a backpacking trip with many people, not just Annie. The fire in the sky was a meteor shower.
John sings "This Old Guitar" near the start of the movie - which is about his successful career. He was not successful however in 1965 and didn't write the song until 1974 for his "Back Home Again" album. So not only this is incorrect because it does not fit the movie. It's like as if the producers didn't even listen to the lyrics.
John cuts the marital bed in half after his divorce from Annie, not as the movie shows as the first step in their breakup.
The movie shows John as having written "Annie's Song" to apologize for his infidelity to Annie during filming of the movie "Oh, God"! Oh God was released in 1977, while Annie's Song was released on John's "Back Home Again" album in 1974 and he never sang in that said film.
The dates of several songs (including "Annie's Song", "Seasons Of The Heart" and "Flying For Me") have been tinkered with to fit the dramatic elements of the story.
The movie implies that John was dropped by RCA shortly after the release of his "Greatest Hits" album, which was released in 1973. Later on in the movie, you will hear John in studio recording of the song "Flying For Me". This song was on John's "One World" album, which was his final album with RCA in 1986.