In the scene where Mary has entered the house of Bruno and stands in front of the painting that he made, she hears Bruno's voice and gets closer to the open doors to look what's going on, one can clearly see that the cast around her neck is missing, yet when she rolls out towards the garden, she's wearing the cast again.
When Edward brings Nora the "deed" to co-sign at the end of the movie, the preprinted information on the document lists the house's address as being in the "State of Utah." All of the other information (street, city, county, and zip code) is for Los Angeles, California, the actual setting of the movie.
During the Mexican Independence Day party,Mary goes up to Bruno to dance. He throws the Birds of Paradise, which she catches. She then says not to waste the state flower, because there's a drought. California's state flower is the California Poppy, not the Birds of Paradise.
The cast on Mary's leg switches from one leg to the other, from when she is wheeled into the house and when she and Nora are in their bedroom then back to the original leg. The reason why the cast on Mary's leg appears to switch from one leg to another is because the initial camera angle in the bedroom is pointed at the mirror (frame around the image), thus causing the cast to appear to be on Mary's left leg. On the next camera angle, it is pointed directly at Mary so it shows the cast to be on the right leg.
When Nora and Edward are kissing in the kitchen, Mary walks into the kitchen and claims to get a fork when she actually grabs a spoon out of the drawer and hurries out of the kitchen. This is not a character error, it's a joke of the movie. She calls the spoon a fork because she is flustered in the moment.