Can someone explain why there is noise on the edge?
I think is an aliasing issue. The edges are where the amount of reflectance changes sharply just like how in a simple cartoon image the edges are where color changes sharply. In both cases, there is high frequency information at the edges.
Let's look specifically at the bottom edge of the car door where there's a little ledge and then the surface of the car goes down again towards the ground.
Notice how in the previous image, at this edge there is a sharp change in color of the car (dark grey to light grey) even though the car (I'm assuming) is painted a uniform color. This is due to sharp changes in the amount of light that hits the surface of the car due to sharp changes in the normal to the car's surface.
If we only take one sample per pixel, we will fail to capture the high frequency change in amount of light hitting the surface of the car at places where there are edges.
At the edges you can see that pixels sometimes get assigned a darker color, because that pixel's sample was taken at a point right before the surface normal changes just enough so that the surface is more directly facing the light source. Other times the pixel gets assigned the brighter color because the sample for that pixel was taken at a point where the surface normal has changed so that the surface is more directly facing the light.
At the edges, pixels span surface areas where the surface normal rapidly changes. Therefore there will be aliasing because the amount of light hitting the pixel will be calculated using only one of the (very different) surface normals it contains.