There were several continuity errors and inconsistencies in the two scenes in Lily's mother's kitchen: the same green bowl with buns in it was in the same place next to the stove in both scenes which took place at least five years apart.
In the second scene, the cactus plant and flower plant on the windowsill change position a few times, and the cactus disappears altogether during the part when 'Molly' is there to visit Lily.
Also, when Lily's mom ladles soup from the pan into the bowl, there's no steam rising from either one. But when the camera angle changes and throughout the scene after that, there is visible steam rising from the same pan on the stove.
At the beginning, in her first letter to Molly, Lily wrote that her dad died when she was three. Near the end, in the police station, she told the detectives she wanted to go stay with her "parents", and they asked where "they" lived, which her boss replied to.