Deception plays a pivotal part in this play by Oliver Goldsmith, but I believe it is more like a motif than the theme itself. Almost all of the characters are involved in some sort of deception, both in the main plot and in the subplots, but one must ask oneself what the author is trying to show through these complicated deceptions. Is deception in and of itself the theme, or does it lead to the theme.
There is much debate regarding whether this play is a romantic comedy, a comedy of errors, a comedy of manners,a farce, a satire, etc. If you do some research on these comedy genres, you will be able to decide for yourself what you think. Then, you will be able to arrive at the theme of the play. What is the author trying to show with these many deceptions? What is he criticizing? Is the play's theme contemporary, or is it more universal?
There is a good analysis of this play right here on enotes. Read the text of the play at the link below.