Problem: If "I put the cake away in the refrigerator. It has a lot of leftovers in it.", is "The cake has a lot of leftovers in it." correct?

Answer: no

Problem: If "Mark heard Steve's feet going down the ladder. The door of the shop closed after him. He ran to look out the window.", is "The door of the shop closed after Steve." correct?

Answer: yes

Problem: If "No one joins Facebook to be sad and lonely. But a new study from the University of Wisconsin psychologist George Lincoln argues that that's exactly how it makes us feel.", is "That's exactly how the study makes us feel." correct?

Answer:
no