1) Being able to paint smooth to help reduce graphical glitches.
If you use contrast levels in the deformation map to do the smooth you would be able to differentiate between 2 definitively different cells and just a segmented piece.
You should be able to paint the contrast change in the 2D view as well.
If any one uses max or maya, I imagine it working like painting animation weights on the model, or using the burn and dodge tool in photoshop.
1.5) Branching off that Idea having an interpolate button to show your final cell with out the segmentation and creases would be great.
2) Another thought would be to have the surrounding cubes toggle on and off. or atleast the first 1/8th of them. Another thought would be just a highlighted general area where your specific cube exits.
3) When you paint an area you can check it by having it compared on the spot with other peoples work, and different parts will show up darker or lighter shades of blue depending on how many other people also painted that. It would be a good teaching tool for people who are not familiar with this type of work. not to mention teach us what we did wrong. And it would explain the scoring.