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.
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.
Walking through the trees (prior to the coastal shots) Girl reveals she is married. Guy asks, "Since when?" She replies,"Two years ago when I became pregnant with Ivanka." This would mean Ivanka would still be a baby (as she is credited) whereas she is clearly a year or so older.