At approx 9:30 into the movie, Guy is exiting the Hoover shop (vacuum repair shop) where he works, and twice there is a mistake between shots of the open/close sign on the front door, once before he says he is going to flip the sign and then once again after he flips the sign, and the shot goes back to the shop and then to the door again.
When the Guy is in the Girl's apartment having dinner and the other tenants come in to watch TV, there is a moment when the chair where the Guy is sitting is visible with out him in it. In the next shot of the seat, he is back in the seat eating again.
When Girl first takes Guy back to her flat, she introduces her daughter to him as 'Ivanka'. Every time afterward that her name is mentioned, it's always 'Ivana'. This is not an error - Ivanka is a diminutive of Ivana.
During the montage towards the end of the film, when the Girl is playing her new piano, the Girl's mother is cooking and stirring something on the stove-top. However, if you look closely, there is nothing in the pan. The mother is stirring the air with a spatula to appear as if she's cooking something.
During a sequence at the recording studio, when the band is performing their song, the drummer quickly looks in to the camera.
In the recording studio, the drums don't have microphones at all although they are mentioned by the sound engineer.
When the girl is walking back to her apartment from the store during the song "If you want me", the crews' shadows are clearly visible multiple times in the sequence.
In the recording studio, at the end of the first song, the boom mic is clearly reflected in the glass behind the Girl.