Hi Brendan, those lines you don't like are just edges of the model, each edge is a spot where there are 2 small surface pieces that are joined together to make a larger structure.

They're the same kind of edges that you'd see on a box where each plane is glued to an adjacent surface piece.

In your case here you probably did a boolean with a cutting curve, and the cutting curve must have been made up of a lot of little segments in it. When the curve extrudes out into a cutting surface you'll get one surface piece for each segment in the original curve.

If you select your cutting curve and use Edit > Separate on it, it will break apart into separate pieces with one piece per segment, that's how you can see the segmentation.

If you drew the cutting curve as one single curve piece instead of out of lots of little small pieces joined together, you would not have all those little edges in there.

You can also use the Rebuild command to reconstruct a segmented curve into a more simple one with only one segment for each smooth piece:
http://moi3d.com/2.0/docs/moi_command_reference10.htm#rebuild

- Michael