At the very end of the movie, Neal the musician is playing his guitar and singing, while the girls are dancing on the stage. Then we see him at the side of the stage, clapping, although we still hear him playing and singing.
At the very beginning when Molly and "Gooey" Huey are talking, Huey says, "That's what I love about you women. You are willing to accept each other for who you are." "Who you are" doesn't match what he really said.
In the last few minutes of the Movie when the song is being played, Neal is playing a standard six-string guitar; however, the sound that's being heard in the movie and recording is from a 12-string guitar.
Around 70 minutes into the movie Neal is talking to Molly and he says "I haven't been able to write a single decent song since we last saw each other". However, his lips only sync up to the "since" part, and he's really finishing the sentence differently. The rest of the sentence sounds dubbed in afterwards.
When Ingrid comes into the apartment after Neal has left, Ingrid says that Molly has 98 messages, but when she picks up the phone she says it is dead, so how could she know that she has 98 messages if she doesn't have any power, plus the phone is dead.
When Molly brings Neal up to her apartment, she ask him to wait in the hallway because the power is out in her apartment, there is no extension cord in the doorway at this time. When she comes back and opens the door to let Neal in you can clearly see the extension cord running on the floor through the doorway by her feet into her apartment.
When Ray's mother is letting Molly go and she hands her the envelope with her final pay in it, the envelope flops down. In the next shot, the envelope is right up again with no evidence that she fixed it in her hand.
Though Molly's electricity has been turned off, she has no difficulty watching cartoons on TV the next morning and her answerphone is working. One of the deleted scenes included on the DVD shows Molly runs an extension cord through her apartment from another and plugs in the TV. While this is not part of the movie that we see, it is a perfectly valid explanation of what we do see.