While filming the "Riddle of the Model" music video, Eamon knocks one of the drummer's cymbals with his guitar while doing a spin. The cymbal vanishes in the next shot when Conor sings at the microphone.
As Conor leaves his house, the day after learning that Raphina has left for London, he's wearing the light brown shoes that he painted black to comply with Brother Baxter's order. In the next scene, they're black again.
In the shots where Brendan drives Conor and Raphina to the harbour, the Mercedes' registration plate is both a different number and style to when they start the journey at home and in the later static shots of the car.
Looking towards Holyhead Conor says on a good day you can see Wales 30 miles away. It's more like 55 miles though, and the farthest you can see is usually about 20 miles.
When the Lawlor family watches the "Rio" music video, Ann asks Brendan "Who is that guitarist" (John Taylor). Brendan responds he is cute, and teases her, but says John Taylor is a bassist, not a guitarist. The video does not show either instrument, and since Ann had never heard of Duran Duran, it is impossible for her to know that he is a guitarist, or a bassist, or whatever.
The Lalor family watches Duran Duran's video for "Rio" - Duran Duran: Rio (1982) - on Top of the Pops (1964). Brendan claims it could go either way as to whether or not they succeed; however, the song was released in 1982 and the film takes place in 1985, by which time Duran Duran was already an extremely successful band and a household name.
At the band's gig, the DJ plays Starship's "Nothing's Gonna Stop Us Now", which was not released until 1987. The film takes place in 1985.
When Conor gives Raphina a lift on his bicycle, they pass a store front with a web address "deafhear.ie" on it. Url's had not been invented then.
During the music video they film in the school, Cosmo mentions the movie Back to the Future (1985); however, Sing Street is based in 1985 and Back to the Future was not released until 20 December 1985 in Ireland. With the time frame of this movie and no indication of him seeing Back to the Future during this time, it makes no sense for him to be aware of what it is.
When the band rehearses in the school hall, the emergency light over the exit door has the 'running man' pictograph. This was not used in Ireland in 1985 and would have only shown the word 'EXIT'.