Several years ago one of my former bosses told me during the interview process that he doesn't get worried when he sees staff members talking in the halls of the church offices. He gets worried when he doesn't hear them laughing.
There is a LOT of wisdom to that statement. Laughter is medically proven to be good medicine. It helps in all kinds of ways that I don't understand and don't need to know except it is is very healthy for the body. And the mind and the soul.
One of the things about laughter is that it means the staff feels comfortable with each other enough to make jokes, share funny stories, and tell self-embarrassing moments. If your staff is engaged in laughing with each other then odds are your staff is not whispering behind your back.
Perhaps the opposite of staff laughter is gossip. Gossip can be serious and vicious and filled with innuendo. Gossip is not good for an organization. Don't get me wrong, I believe in the office grapevine and use it, but that is different than gossip, especially malicious gossip.
Encourage your staff to laugh. Find ways to make them laugh. Get them to tell stories on themselves (but never a story that embarrasses someone else). Listen to the halls of your office. If you don't hear laughter on a regular (several times a day) basis, you need to worry and find ways to get your staff to laugh - together.