There are plenty of examples of appearance versus reality in The Scarlet Letter by Nathaniel Hawthorne. The most significant one, it seems to me, is the fact that the pious minister, Arthur Dimmesdale, is actually an adulterer who had an illicit affair with a married woman.

Throughout the novel, a war between his soul/spirit and his body rages. He is a sensitive man to begin with, and then the constant conflict between what he knows he should do (public confession and repentance) and what he does (private punishment and condemnation) causes his body to deteriorate.

“I have laughed, in bitterness and agony of heart, at the contrast between what I seem and what I am!” 

In chapter twenty, we see an excellent example of the dual life Dimmesdale leads:

No man, for any considerable period, can wear one face to himself, and another to the multitude, without finally getting bewildered as to which may be the true.

As he walks back into town in chapter twenty, he sees things--or thinks he sees things differently. It is unlikely that anything in town has really changed, so it is probably how he looks at things that has changed--but we are not sure.

A similar impression struck him most remarkably, as he passed under the walls of his own church. The edifice had so very strange, and yet so familiar, an aspect, that Mr. Dimmesdale’s mind vibrated between two ideas; either that he had seen it only in a dream hitherto, or that he was merely dreaming about it now.

Another example of appearance versus reality in the novel is the relationship between Roger Chillingworth and Artur Dimmesdale. The people, of course, are thrilled that their beloved but weakened pastor is now living in such close proximity to a doctor; however, we know that Chillingworth is also Hester's husband and has an agenda of revenge. Eventually the people sense that something is not right, but they do not know why:

it truly seemed that this sagacious, experienced, benevolent, old physician, with his concord of paternal and reverential love for the young pastor, was the very man, of all mankind, to be constantly within reach of his voice.

What they see and what he is are quite different, and appearance certainly does not reflect reality.

Finally, the puritans themselves are a great example of appearance versus reality. While this is a community which claims to be "pure," the citizens certainly do not act like what they claim to be. The women scorn Hester but continue to give her their sewing projects, and when she delivers their things, they scorn and insult her. While they claim to be Christians, they teach their children to vilify both Hester and Pearl.

The most vivid example of this is the crowd as they speak about Hester at the beginning of the novel. Again these women claim to be Christians, but this is an example of their conversation about Hester:

“The magistrates are God-fearing gentlemen, but merciful overmuch,—that is a truth,” added a third autumnal matron. “At the very least, they should have put the brand of a hot iron on Hester Prynne’s forehead. Madam Hester would have winced at that, I warrant me. But she,—the naughty baggage,—little will she care what they put upon the bodice of her gown! Why, look you, she may cover it with a brooch, or such like heathenish adornment, and so walk the streets as brave as ever!”

There is no compassion, no sympathy, and no grace; there is only condemnation, scorn, and bitterness. These are not the hallmarks of Christians.