When Melinda first meets Dr. Landy in his office, his watch reads 4:55 but his watch then reads 4:40 for the rest of the scene.
When Brian jumps off the sailing ship with Melinda, he's wearing tennis shoes and plain white socks. However, when he walks ashore, he's wearing blue (or grey) socks.
When Brian persuades Melinda to jump off the boat (near his house), he is wearing shoes, yet when they emerge on the beach he is only wearing socks.
Contrary to what is shown, the recording for "Good Vibrations" began during the making of "Pet Sounds", not after.
Dialogue suggests that the "Smiley Smile" album was completed by the Beach Boys without Brian's involvement; archival tapes show that he was actually very involved in the album's recording.
It is implied that Wilson dropped acid for the first time shortly after the release of "Pet Sounds". In real life, Wilson first dropped acid in the early spring of 1965, a year before "Pet Sounds".
In a scene which presumably takes place in 1967, Murry Wilson tells Brian that he has sold off the band's publishing company. In real life, Murry did not do this until 1969.
Van Dyke Parks claims that he had been writing lyrics professionally since he was 14-years-old. While the real Van Dyke Parks began his professional career as a child actor, it wasn't until 1964 (at the age of 21) that he began taking an interest in songwriting and composing.
Brian tells Melinda when they are sitting in the Cadillac in the showroom that his brother died two years earlier. Dennis drowned in December 1983. That would make the scene set in 1985 or early 1986. The song playing in the background is "Songbird" by Kenny G, which was not released until 1987.
In the studio, the baritone saxophone player is seen with a Yamaha baritone saxophone. Yamaha didn't make baritone saxophones until 1969.
When Melinda and Eugene are talking outside about Brian, camera crew members are reflected on the side of Melinda's car.
When Brian talks about a Shanty album while inside the pool, by the end of the scene a crew member is reflected in the window behind him over his left shoulder.
During one of the pool scenes, Mike Love demands that he and Brian throw away the "Smile" lyrics and rewrite them as "normal" Beach Boys songs. In real life, some of those songs *were* rewritten for the "Smiley Smile" album, but they weren't any closer to being "normal".
In a scene while Brian and Melinda are having dinner, Brian says that he hasn't seen his daughters in two years and Melinda responds with surprise that he has two daughters, but he didn't tell her how many daughters he had.