Maggie can sense if a person is lying to her or to someone else.
Maggie can sense a lie by being in close proximity to someone. A person didn't have to speak for her to know if he or she was behaving in a way contrary to their beliefs. If anyone misrepresented themselves in either appearance or action, Maggie could feel it automatically.
However this also has a side effect, as any kind of deception made her physically uncomfortable.
When Maggie was human, she always knew when a person was lying with their words, which compelled her to always point out the lie. This made others feel uncomfortable around her as they could never lie in her presence, prompting her parents to leave her behind when they immigrated to America.
When Maggie and her coven is approached by the Cullens' cry for help, Maggie senses their honesty and agrees to be their witness against the Volturi. After Alistair - one of the witnesses - fled for fear of the Volturi, Maggie still decides to stay behind and help.
Charles can sense whether a person is lying to him. It has not been explained how different from Maggie's this gift is, but it appears to be less pronounced than hers.
When Charles is first approached by the Volturi's offer to witness their punishment on the Cullens, he senses no dishonesty from their behalf and so complies to their wishes. However, when he and his mate, Makenna, arrive in Forks, Charles senses the Cullens' honesty in their testimony, being falsely blamed for a crime they did not commit, and also newfound dishonesty from the Volturi. He gives his witness and then leaves with his mate.
Aro's ability of tactile telepathy allows him to read people's minds and determine if they were telling the truth as well as access to every thought they ever had.