When ambulance arrives for Bernard, it is clearly daytime. When he is placed inside and it departs, it is night.
The Squid and the Whale display in the museum is in reality not brightly lit. It is a very dark display meant to simulate the inky depths of the ocean. (It probably would not show up on film as it really exists.)
When the Berkmans are speaking to Walt's teacher about his plagiarism of the song "Hey You" by Pink Floyd during his performance during the talent show, there is a poster behind the teacher promoting reading featuring the WWE wrestler Hurricane (Shane Helms) who made his WWE debut in 2001. He was only 12 in 1986.
The ambulance that takes Bernard to the hospital after his heart attack has the 9/11 memorial logo (Twin Towers) on the back.
At the end of the movie, Walt enters the newly renovated marine exhibit of the Museum of Natural History through the Hall of Biodiversity, built in 2000-2001.
When Walt visits his father in the hospital, there is a Purell Anti-Bacterial Hand Dispenser on the wall in the background.
When Walt is learning 'Hey You' from the record and from the book, the book has the song in standard music notation and in tablature, but tablature was just starting in the guitar magazines of the mid-1980s and the style of the book is also from a much later date.
When Bernard is in Walt's room, telling Walt he should see a psychologist, a boom microphone arm is visible in the reflective surface of Walt's guitar.
Frank complains that the writing desk Bernard got for him is for a lefty. Frank is clearly a lefty, as evidenced in his eating, drinking, tennis and ping-pong play.
Bernard misrepresents the end of Breathless (1960): he says that Michel says "You're a bitch!" to Patricia at the end; actually, Michel says "It's disgusting," then Patricia asks Detective Vital what Michel said, and Vital misreports it as "You're disgusting." It's unlikely that someone with such a deep interest in art house film would get it so wrong.
The close-up of the letter Frank receives says "Mr Beckman" twice not "Mr Berkman".