Falcon: The proud bird is a symbol of Katherine.  After Petruchio marries her, he has to figure out a way to make her into the wife that he wants.  To do this, he trains her like he would train a falcon.  He denies her food and sleep until she is willing to do anything that he wishes.  He also shows her prizes such as clothing and food which she desires, and then takes them away. She, like the bird, comes to depend on him for these things and realizes it is her duty to love and serve him.

Christopher Sly: Like Baptista Minola, Christopher Sly believes anything that the Lords tell him.  He readily takes in the tutors and accepts their identities.  He also accepts Tranio as Lucentio without any sort of questioning. 

The Sun and the Moon: The last real battle that Petruchio and Katherine has is about what is lighting the sky, the sun or the moon.  It is the middle of the day, so Katherine says it's the sun.  Petruchio on the other hand tells her it is the moon.  The moon tells that Katherine is still in "the dark" or "nighttime" about her behaviors and duties as a wife.  When she finally agrees with him, Petruchio says that it is the sun after all, symbolizing the fact that she has realized her duties as a wife.