When Alex and Sophie are at breakfast, Sophie's cup changes positions several times between shots. Many times, she will lift the cup to take a drink, then in the next shot the cup is back on the table.
When Alex and Sophie are having breakfast, Alex has a muffin. When you see him talking to Sophie facing her, you see his muffin. It goes from eaten out of to untouched repeatedly during the scene.
When Alex and Sophie are walking by the bookstore, you can see Sophie's hair looks like her hair color is growing out half-way down her head. Scenes after that show her hair is fully one color.
Watch the ring on Alex Fletcher's hand. It changes between the middle and ring finger multiple times in the movie.
In the bakery scene, Alex's muffin switches from being on a plate to being on the table several times.
When Alex and Cora are singing "Way Back Into Love" at the concert, there is a shot of Chris and his daughter in the audience, and they turn to look at each other and smile. The video of this clip has been reversed (it is playing backwards); you can tell by watching the people clapping behind them, and the daughter's hair as she turns her head.
When Alex and Sophie are in the piano store and he is trying to convince her to become his lyricist, as he is playing a piano, the camera reveals the inside of the piano, where the piano's hammers are not moving even though music can be heard coming from the instrument.
Sophie and the woman with Chris at the restaurant switch outfits to make Sophie look better for Sloan. The woman is about 6" taller than Sophie but both sets of clothing fit both of them perfectly.
When Alex and Cora are singing "Way Back Into Love" at the concert the song is missing the last additional four lines and final chorus.
The video for "Pop Goes My Heart" is given a year of 1984, but the top keyboard being played was the Roland D-50, which did not come out until 1987.
In the video clip featuring Alex Fletcher in "Pop Goes My Heart," an automated infusion pump system is visible. That kind of intravenous drug administration systems weren't yet available in 1984.
Another instrument anachronism: In the video for "Pop Goes My Heart," the bassist is shown playing a Steinberger Synapse series bass guitar. While aesthetically somewhat similar to Steinberger models in the 1980s, the Synapse line wasn't released until the 2000s. (Also of note: He's playing a right-handed bass left-handed, but this is somewhat common considering that many models of guitar are and have been unavailable left-handed.)
There is a scene where Alex and Sophie are walking to the coffee shop. The camera is traveling behind Sophie and Alex but you can clearly see that the audio is not synchronized with the movement of Alex's lips.
During the scene where Sophie and Alex are in the café and he sings "I've got sunshine on a cloudy day..." When it cuts to the camera viewing Sophie, you can see that his lips are not synced with his vocals.
In the studio recording the additional verse that Sophie had finished, they're recording it in the relatively "dry" version that they eventually sing during the concert; however at this point in the story Sophie and Alex are estranged because Cora is planning on a "steamy and sticky" version of the song.
When Chris is pitching Greg Antonsky to Alex by saying he's "just worked with Avril", he mispronounces Avril Lavigne's first name. A manager in the music industry in 2006 would know perfectly well who Avril Lavigne is and how her name is pronounced. It's pronounced 'av-ruhl', Chris pronounces it 'ah-vreel'.