When Lucy is kneeling beside her grandmother and says her heart was not very strong and said she is so sorry, you can clearly see grandma's chest rising and falling. She was breathing and still alive in the scene.
For the artwork, when the American flag is hung vertically, the "blue" field with stars should be in the upper left hand corner. In this case, it is reversed.
When Jose and Lucy are walking through the train station you see they are on the Church Ave platform. This would exit to Church and McDonald Ave which is outside of Bushwick. When they get to ground level they are now in Bushwick on Starr and Wycliffe Ave.
If Lucy is a second year graduate student, she would be 23 at a minimum, not 20 years old.
When Lucy is a bodega the owner can still be seen breathing after he dies talking.
Lucy is in her Grandma's house on the bed and she is now wearing a green coat instead of the red plaid she wore entering the house.