My ducks have free range of my entire acre, which includes lawn, trees, bushes, garden area and some flower beds.
They do eat the slugs out of my flower bed, and will eat the plants they like. As far as the garden, I keep it fenced with that plastic garden fencing. It's not very tall and keeps them out nicely. Ducks will (in my experience) also "aerate" your lawn for you! They can and do dig little holes in the lawn (digging for worms/bugs) up to a few inches deep. It almost exactly resembles the little holes when a lawn is aerated! I don't mind it, but some people might.
They will eat anything they find tasty; all kinds of bugs, plants, flowers. They don't always know what is poisonous or not good for them. One day a styrofoam cup had blown in to my yard. I found the ducks and chickens happily tearing it up and eating it! I need to paint my garage, and the the bottom part is peeling a little. The chickens peck and eat the paint chips! There is a reason for the saying "dumb cluck!"
Hope that gives you an idea.
I love having my fowl. They are entertaining and pull their own weight around here with my little egg business.