Other mistake: Alicia Witt's character is introduced as June CARVER, but at the film's end titles (and also on the DVD's cast list screen) she is billed as June CARTER. On the audio commentary, writer Marc Lawrence explained the name change... but it seems that he forgot to let the titling people know. (00:47:05 - 01:32:25)
Other mistake: In the final scene, George is "shocked" how small the apartment is, but he shouldn't be surprised since he has been there before (when he went there for cake). (01:37:50)
Suggested correction: When they are eating cake on the roof it is at Lucy's parent's apartment, not hers. So he is really shocked when he is in her apartment.
I apologize, for some reason I thought it was her apartment.
Not so - in an earlier scene she mentions how she's 'back at her parents' house' (while phoning the Chinese place). She lived there prior to being given a nice apartment by George as a perk of the job. After resigning, she moved back there. Therefore the goof is valid.
No, it's her parent's apartment. She says she is staying there, you see her there with her Dad in the morning, George says "thank goodness your parents went to the movies. We'd never have all squeezed in" and she's ordering Chinese food from the same place she ordered from when she said she was staying at her parents. George may not have gone in when they got the cake, or he might not have noticed the size.