In Ollie's office, there is a poster in the background for Songs: Ohia's "Ghost Tropic" album, released in 2000. The scene takes place before Independence Day was released in 1996, before Songs: Ohia had even released their debut album.
In the first scene, at the Christmas party, Santa Claus is sitting on the throne in the middle of the room with a girl on his lap. When Ollie walks up there seconds later (in the next shot) they are both gone.
When Ollie feeds his daughter when he first moves in with his father, there is milk running down her cheek. He then places the bottle next to her. In the next shot, there is no trace of milk on her cheek.
After their argument, Ollie goes upstairs and sits on Gertie's bed. He finds out that his daughter sleeps with her mother's pictures. Ollie picks up the picture from Gertie's hands, and after she wakes up and they speak, Ollie gives the photo back twice.
While Gertrude is putting on her earrings during her fight with Ollie, she leaves the room without having put the left earring on. In the next shot of her in the next room, there is an earring in that ear.
Gertie's gravestone indicated she died (in childbirth) on June 1, yet she was extremely pregnant in the scene where she was preparing to attend the Video Music Awards, which are held in late summer/early fall. Ollie and Gertie should have been preparing for the MTV Movie Awards, or else Gertie delivered about 6 months overdue.
When Ollie picks up Gertie at school and they are discussing about Cats, as the camera alternates shots between Ollie and Gertie you can see the background moving at different speeds (slower for Ollie, faster for Gertie).