Photos would be helpful -- I'm not really sure what you mean when you say you have pits in your soap. Here's what I have encountered in my soap making --
When I cut my soap with a wire cutter, the cut surfaces are bumpy. I think the bumps are caused by tiny lumps of slightly harder soap that pop out of the surface of the soap during the cut. I don't see these bumps when the soap is cut with a blade because I think the blade smears the lumps flat, but I nearly always see bumps on the soap when I cut it with a wire.
The first image of an ivory colored soap shows the bumpy surface after being cut by a wire. If I don't want the bumps, I plane a thin shaving off the cut faces and that solves the problem.
I think it's also helpful to cut the soap when it's firm like colby cheese -- not soft like brie and not hard like aged cheddar. And also tighten the wire so it makes a definite musical note when it's plucked like a guitar string. But even when I take my own advice, I still see the bumps.
I also sometimes see small holes too that are caused by air bubbles in the soap. This is caused when air gets beaten into the soap and most of the time I think it's how I use my stick blender. This is a (mostly) preventable problem -- don't whip air into the soap.
The second image of a golden colored neem soap is a closeup of what this looks like. This soap was cut with a wire and then planed, so you don't see bumps anymore, but the tiny craters from the air bubbles remain. The white spots are probably air bubbles that aren't cut open. The bubbles aren't nearly as obvious when you look at the real bar -- I've really blown this image up so you can see the detail.
