What is the significance of smiling in Julius Caesar?

It seems to have been one of Shakespeare's favorite observations that just because someone smiles does not mean they are innocent or friendly. In Act IV, Scene 1, Antony, a "shrewd contriver," recognizes the danger in the many seemingly friendly people he sees around him. And Octavius agrees as follows:
And some that smile have in their hearts, I fear,
Millions of mischiefs.
In the conference on the battlefield at Philippi of Antony and Octavius with Brutus and Cassius in Act V, Scene 1, Antony describes how all the conspirators were smiling just before they turned on Caesar:
You show'd your teeth like apes, and fawn'd like hounds...
In Macbeth, Act II, Scene 3, Donalbain tells his brother:
To Ireland, I; our separated fortune
Shall keep us both the safer. Where we are

There's daggers in men's smiles: the near in blood,
The nearer bloody.
Hamlet seems to make an important discovery about human nature when he reflects on the interview he just had with his father's ghost in Act I, Scene 5.
O villain, villain, smiling, damned villain!
My tables—meet it is I set it down
That one may smile, and smile, and be a villain.
Shakespeare has given all of us fair warning that we shouldn't always take people's smiles at face value.