When Christine first leaves to visit her fathers grave, she has pink and white flowers. When she arrives at the grave, she has only five red roses.
When Christine visits her father's grave, we see several close-ups of the black wrought iron gate surrounding the cemetery. In these close-ups, you can plainly see that the wrought iron is actually wood that has been spray painted black.
When Christine first starts singing to the phantom in front of the fireplace near the beginning, her voice doesn't match her lip movement.