Also try every path effect.

There are hundreds of curves in this picture, but you don't see anything.....

Nah, curves wouldn't have made it really harder.

This is just the way Inkscape draws filled polygons on a bitmap canvas, not really a bug. It draws them sequentially with edge antialiasing achieved through alpha-blending the polygon's color with what's already drawn on the canvas.

Let's say you have two polygons, each covering a half of one particular pixel. The first polygon's edge is blended 50/50 with the background, leaving 50% of the background color visible. The next polygon is blended again, and since it also takes up 50% of the pixel's area, the background color is halved again, which still leaves 25% of the background bleeding through. If the two polygons are touching, they should completely obscure the background, but due to Inkscape's method of rendering polygons, some of it remains visible.

The problem could be avoided by simply adding the partial areas the polygons cover to the pixel value instead of alpha-blending them, but it's not that easy. Such a process must be numerically robust in order to avoid overflow (this can be handled in several ways). The polygons must not overlap (overflow again, but now certain, and meaningless values)— this particular problem could be resolved by using boolean operations, namely subtraction and OR: OR the polygon that's just been drawn with the already ORed bunch that was drawn before, subtract this conglomeration from the next one, draw the result, repeat.

Well, as you can see the whole process is computationally quite expensive and ridden with other problems like handling non-solid coloring or mixing plain polygons with objects with some bitmap filter applied to them (blur, for instance). I guess it's not suitable for real-time rendering, but it could be used in export. By the way, about a year ago, when I was still obsessed with programming my own polygon-filling routines, I looked into this very problem, found the flimsy solution I just described, and, with the help of the Clipper library, implemented it in a tiny 2D polygon renderer I wrote in C. It worked… tolerably well. Perhaps there are better solutions.

By the way, you can mitigate this flaw by exporting your drawing at a humongous resolution and then scaling it down.