Here are some of the things I have learned so far working with the Cricut Cake:
The material you use is key. Gumpaste works very well, modeling chocolate works well too. Fondant on average is just too mushy, but I had good luck using Fondarific. Next time I will test fondant mixed with Tylose to see what happens.
Thickness (or thinness actually) is very important also. On the blue and brown cake (below) I left the modeling chocolate too thick. I still liked the overall effect, but I had to cut a lot of extra pieces and clean the blade several times. On the "Chuck" cake, Chad rolled out the gumpaste so thin you could almost make out the mat under it. They cut out very nicely.
My last finding was that no matter the material I used to cut on, popping it in the freezer for 5-10 minutes before cutting always yielded better results.