I would say that the main theme centers around morality. There are distinct groups of characters - those who are members of the "school for scandal" and those who are not. In the first group, we see characters who maintain a facade of morality (or "sentiment"), but who spend their days gossiping and manipulating to destroy others. These are the members of the "school for scandal" - Lady Sneerwell, Joseph Surface, Snake, Sir Benjamin Backbite, etc. In the moral group, we see Peter Teazle and his friends, who try to live morally and uprightly. Then there is a group that doesn't fit either category. Charles Surface and his friends; this group behaves badly (drinking and womanizing, etc.), but makes no excuses for it.
Sheridan paints the first group as the most corrupt and the ones who rightly deserve the punishment they receive (banishment from society) when their duplicitous ways are discovered by the end of the play. Lady Teazle is forgiven for consorting with them, as she is genuinely apologetic and contrite. Charles, who is nothing but honest, is rewarded for that, in spite of his immoral behavior.
I believe Sheridan's main message is about being truthful and upfront, not playing games with others' feelings. The play, which is a Sentimental Comedy, can very much be seen as reaction to the excess of the English Restoration.