There are a number of examples of misconception and illusion in The Great Gatsby.
The most poignant example may be Wilson's fatal misperception of the car accident that killed his wife, Myrtle. It was Daisy who was driving Gatsby's car and who ran down Myrtle on the road, but Wilson believes that Jay Gatsby was driving.
This misperception leads to Gatsby's murder and is a clear example of a character's perception differing from reality.
Another example of the dynamic of misperception comes where Nick finds the drunk man at Gatsby's party looking at the books in Gatsby's library. The man believed that the books were fake and probably made of cardboard, but when he investigates the book shelves he discovers that the books are real. This investigation parallels Nick's relationship to Gatsby.
At first he doubts Gatsby's story and his honesty then he is won over and begins to believe in Gatsby. Finally, he learns the truth about Gatsby, who he is and where he has come from. For a time however, Nick's view of Gatsby is another example of a perception differing from reality.