Ducks and geese get their faces all dirty by drilling in mud and in their food. You can do the five gallon bucket with the holes in the lid if the ducks are tall enough to reach down inside. I made one out of a plastic coffee container yesterday for my hatchling geese. They think it's pretty cool. I buried it about halfway in shavings so that it's not too tall for them. They do get it dirty, because their bills are dirty from sticking them in the food. There's nothing short of giving them running water that will fix that. It won't hurt them. It's just their food and a few shavings that made their way in, what with babies climbing all over it.
My adult ducks and geese drink out of buckets. They don't climb in them, but they dunk their heads. The buckets get gunked up fast with mud (they like to drill their bills down into any mud they can find, then wash off in the buckets.) IMO, a lid for the buckets, with holes in, would only make it harder for me to clean the mud out. I swirl the water around to pick up the sediment, dump it out, then dip out new water from a tub under the downspout. It's tall. Not even the geese like to drink from it (though they can), so it stays fairly clean.
They also have a wading pool. I spray it out, fill it up if I have time and feel like doing it. They enter with joyous abandon, splash most of the water out and make the remainder filthy with mud and poo. There is a little seasonal brook and they have fun in that, but they don't make it filthy because the water is running through. Running water is the only clean water around any waterfowl--from the most regal swan to the lowliest ugly duckling. It's the way of ducks and their kin. For this reason many people choose not to raise them. I like them, though. We're on 12 acres. If we were more crowded I might feel differently.