Hi Tarnis,
The texture compositor looks at the textures and the geometry to determine if these textures tile. If a texture tiles, and you want to composite a tiling texture, then it must make sure that the tiling texture’s edges in the tile direction touch the edges of the composite texture.
The problem you are seeing, is the tool thinks that one of your textures tiles, when you do not. I would look at the uvs for the polygons that use each of those textures and make sure that they do not go out of the 0-1 range. It could be that one of the polygons mapped with that texture just barely is out of range (ie 1.0001 instead of 1, or -0.00001 instead of 0). It could also be that one of the textures is mapped completely out of range. (ie 1-2 instead of 0-1).
A quick way to figure this out is to select all polygons that have each of the textures one set a a time, and look at the uvs in the uv editor. (ignore the textures that are smaller in width than the widest one, because that can’t be the one that tiles) To do this, deselect all polygons. Then select the image in question from the texture palette. Then run the select similar texture from the select menu. This will select all polygons that use that texture. Now you can run the uv editor, and see where all your polygons are mapped. Make sure you normalize all polygons so they are in the 0-1 range, then zoom in on the corners to make sure they do not exceed the 0-1 boundary. Then just repeat this until you find the offending texture.