Anti-aliasing is the technical term to describe how a computer program adds a "blur" to lines. This blur helps the human eye see an image more smoothly, but interferes with how Wargear floods a territory in fill mode.

The blur is achieved by adding semi-transparent pixels of the same or similar color as the line you are drawing immediately adjacent to that line. The Wargear engine floods all of the congruous pixels of the same color, so when the flood gets to your blurry Anti-aliased pixels it sees them as something else, and leaves an ugly, fuzzy, usually grayish ring around your territory. Its ugly, and should be avoided whenever possible.

Here is a handy infographic which explains in pictures where the option for turning AA on and off exists in Paint.Net, what tools are affected by AA, and by what other names similar functions in Paint.Net go by. It also includes a quick sketch illustrating an image drawn and filled with AA on alongside an image drawn and filled with AA off, so that you can see how your board will look in game.

Once you've mastered AA management to keep your fill floods crisp, I suggest you play around with using layers with the background drawn with AA on, and a higher layer for your flood areas with AA off. This way, your fills will flood as intended, but other areas of your map will still appear smooth.

As a tangent, the file format you choose to save your work can affect the final results of your uploaded image as well. I'll save that discussion for another post, but simply put: Always save as .png. You won't have any problems.

FAQ:

This space reserved for FAQ

This has been added to a Help page http://www.wargear.net/help/display/Fill%20Mode%20-%20Anti-Aliasing (Lastly, awesome write up Cram!)
Any objections to unstickying it?
And make a single Sticky with Dev Testers/FAQ?

go ahead and unsticky