When Dan is talking to Gretta on the night they meet there is a girl walking up the subway steps. When the scene cuts to a different view the girl disappears.
When Gretta and Dave are in the kitchen and listening to the song he recorded in LA the clock under the kitchen counter is at 9:45 at the beginning of the song but when Gretta is unplugging the speaker the clock is 11:38.
When recording the song on the roof Miriam is apparently recording or taking photographs of the session as you can see her walking around the band. About 40 seconds into the song she just appears behind the band only to disappear a few seconds later.
When Dan is talking to Saul, Saul's lapel pin is upside down, then right side up in the next shot.
When they're walking together sharing the music with a splitter, shortly after the Stevie Wonder song starts, the camera cuts to behind them and the splitter with the headphone wires disappear then reappear when the camera cuts back to in front of them.
When Dan (Mark Ruffalo) and Gretta (Keira Knightly) begin practicing for the album with the band in Gretta's apartment, they have the full band in that scene including their drummer and bass player. In a later scene Dan and Gretta go to see Troublegum (CeeLo Green) to ask for a favor - they need a drummer and a bass player! The same drummer and bass player are seen before and after Dan asks Troublegum for help finding them.
When they are recording the first live song (about 54:53) in the alley, Dan's camera still has the lens cap on while he's taking photos.
When they are recording on the roof, the song comes to an end, with Violet playing the last notes, but Dan is still strumming on the bass guitar; there is no bass guitar playing at the moment.
When Dave Kohl wins the Music Gong and Gretta, Steve, and Dan watch the video on the laptop, the audience screams out "Levine".