Hi Cathy,
Swales generally are not mucky. They are just an area of the lawn that look like a channel but that are really not very noticeable. The purpose of a swale is to take water away. It sounds as if yours is not functioning properly. This often happens if there is not enough pitch to the swale. In other words, the elevation should get lower and lower.
Sometimes also a swale can be too deep and narrow and grass will not grow.
If I am on the right track, you have two options. The first would be to widen it , regrade so that it has the correct pitch (the water will then not sit there but keep moving to a destination), and re-seed the area.
The second option is to clean it up and fill it with decorative stone. This then changes its function from a swale to more of a drainage pit/ditch. The soil below should be porous enough to allow water to seep into the ground. Clay soil will defeat the purpose as it is difficult for water to permeate through this type of soil. The stone on top will also allow infiltration to below.
You can then choose to plant at the edges in whatever areas you like...or even all of it.
