What are three examples of appearance versus reality in Shakespeare's Othello?

First, let's define what we mean by "appearance vs. reality." It's first important to understand how Iago functions in the text as the main source of drama. Thus, an example of his personality will be our first example. The following two examples will talk about appearance vs. reality via examples in the text when characters are deceived (by Iago) as to how events occurred and whether or not they actually occurred at all. As Othello is a play based on misunderstanding, noting two moments of misunderstanding will help understand how the play's characters are deceived and how this play is thus called a tragedy.

Our first example is that Iago appears to be loyal to Othello, but in reality he is deceiving them. Iago states explicitly:

"the Moor is of a free and open nature/ That thinks men honest that but seem to be so; and will as tenderly be led by th' nose/ As asses are" (2.1.391-4)

Them are fightin' words! Iago just called Othello an ass. Not very friendly.

A second example is when Othello thinks that Cassio and Desdemona hooked up because Cassio has Desdemona's handkerchief. Othello loses his cool and passes out right after saying:

 "Lie with her! lie on her! We say lie on her, when 
  they belie her. Lie with her! that's fulsome. 
  —Handkerchief—confessions—handkerchief!—To

confess, and be hanged for his labor;-first to be

hanged, and then to confess.—I tremble at it. 

Nature would not invest herself in such shadowing 
passion without some instruction. It is not words 
that shake me thus. Pish! Noses, ears, and lips. 
 —Is't possible?—Confess—handkerchief!—O devil!" (4.1.35-43)

Now, Desdemona didn't cheat on him. Iago had his wife Emilia swipe Desdemona's scarf after she drops it on the ground by mistake. Sneaky, sneaky.

A third example is when Othello treats Desdemona like a whore because of what he believes she did with Cassio. He says:

" She says enough; yet she's a simple bawd 

That cannot say as much. This is a subtle whore,

A closet lock and key of villainous secrets 

And yet she'll kneel and pray; I have seen her do't." (4.2.20-3)

Othello is enraged at what he perceives to be Desdemona's behavior.