What hypocrisies do you find in the nun in "The Canterbury Tales"?
For one thing, she owns all these dogs and animals that she feeds with roasted meat and milk and bread--she feeds them better than the poor to whom she should be devoting her attentions.
For another, she is "overgrown" herself. Chaucer and other medieval folks believed that the clergy and servants of the church should not show wealth in any way--those who served the Lord should not be fat indicating an abundance of food, nor should they be pale--indicating a lack of laboring outside in the cruel sun. However, it is understood that not all nuns had jobs that required them to labor outside in gardens, etc.
In addition, her lips are red and her jewelry is engraved with "Love conquers all". Perhaps Chaucer is attempting to tell us that she is not a true nun after all. Her manner is flirtatious and more feminine than a nun's should be...in this manner, we can interpret her engraving in two ways. Love=Jesus and that true Christian love does conquer all; or Love in the flirtatious, human and feminine way gets her the thing she wants and thus conquers all.
There are other more minor things--her French is not perfect as is implied, and she attempts to act above her station in a courtly manner as the members of a royal court might behave and this is not approved of for nuns.
Only the Knight, the Parson, and the Plowman are wholeheartedly approved of by Chaucer. Pay close attention to your footnotes as you read for hints!
More hypocricy can be found when looking at the nun herself and her tale. Don't you find it a bit ironic how her tale includes such vulgar imagery and isn't at all what you would expect from a nun? The tale is about a young, innocent boy who get killed, you'd expect something quite different. Despite the fact that he's singing a religious song, the tale also seems to imply religious prejudice between the different religions.