How are the themes of illusion and truth portrayed in The Merchant of Venice?

"Appearances can be deceiving" is a major theme in The Merchant of Venice. It is brought out most obviously in the subplot with the caskets. Portia's father has stipulated in his will that all her potential suitors must choose between three "caskets" (actually small chests): one of gold, one of silver, and one of lead. Portia's picture is in one of these. If a suitor chooses the right casket, he can marry Portia.

The reader will easily guess that Portia's picture is in the casket of lead. The suitors are not familiar with this game, though, and the caskets also come with little poems that seem to hint that the picture is in each one.

In Act III, Scene 2, Bassanio (who Portia actually loves) chooses a casket. Portia is tempted to give him a hint, but she refrains. Luckily, he chooses the lead casket. His reasoning is as follows:

But thou, thou meager lead,

Which rather threaten'st than dost promise aught,

Thy paleness moves me more than eloquence.

Here, Bassanio is talking to the leaden casket as if it were a person who is not pleading with him, but is looking pale as if in the grip of some emotion. Just as a perceptive person might be able to look at someone in distress and discern their emotional state, so Bassanio deals with the casket.

Before choosing the casket, Bassanio gives a speech about this very theme. It begins, "So may the outward shows be least themselves" (line 73).

This theme becomes even stronger later when Portia dresses up as a young lawyer so she can go to court and save Antonio's life. Bassanio, despite his perceptiveness, does not recognize her. In the argument she makes, she sticks strictly to the law and the words of the contract (the "bond"), which at first appear to give Shylock the right to take a pound of Antonio's flesh, but which on closer examination don't, and in fact give Antonio the right to take all of Shylock's property. 

The theme of illusion is taken to comic lengths in Act V, Scene 1, when Portia and her maid Nerissa play a prank on their husbands, Bassanio and Gratiano, who never did recognize them when they were dressed as men. It goes so far that the wives threaten to sleep with these "young men" (actually themselves), and their husbands threaten to harm the men. When the joke is finally revealed, Bassanio and Gratiano are surprisingly quick to pick up on it, and are surprisingly good sports about it.