Meshrepair utility has a 'match mesh edge' function, which can be followed by a Join command.
Their might be a mesh Patch command that will work or you might have to make some curves from those edges to build some connecting geometry.
If you're rendering at the size shown above it's going to be quite hard to not get problems with stepped edges like you have on the counter tops - they're just at a bad angle for the resolution this image is rendered at, it's just a limitation of how many pixels you have to work with. You need to have overlapping edges/meshes as far as Im aware. The problem is if you've got any grain for example, the anti aliaser might see it as an edge and make it more visible.
Lastly, use the V-RAY RT renderer to your advantage. Here's catmull rom, here it actually darkens the pixels either side of your edges so it has more contrast and appears sharper. Adjust lights, camera settings and material properties (diffuse values, reflection, refraction). This is the gaussian filter, the middle of it is the pixels being anti aliased, the sides are the edges around it - what this filter does is softens the pixels arond so they gradually ramp together - it's blurring the area where they meet. On this page you can see a lot of different diagrams that show how this contrast is applied. If you've got a dark and a light edge meeting, it'll darken the row of pixels on the dark side and brighten the light ones to give them more contrast and thus more defined to your eye. What the catmull and other sharpening filter does is a colour correction wherever edges meet. To be honest I don't know if there's a major benefit in doing this - it was discussed before and vlado mentioned you're not going to get higher quality out of it or any speed benefits.