That's the result of two anti-aliased edges of a vector butted up against each other. Anti-aliasing smooths the edges of a shape for on-screen viewing by using different levels of transparency on each pixel based on how far inside or outside of the edge each pixel is.
So when you butt up two shapes against each other, some pixels along the edge get a little bit of transparency from each shape, but not enough to be fully opaque, so the white background behind the shapes shows through along the edge. It won't normally affect your print, but it might if you were to rasterize before sending to your RIP, which it seems you may have done, since you're saying the dots get bigger when you zoom in.