Yepp, clip brushes are filtered out by default. You can enable them in View \ Filters menu.
The other ones Lil Killa mentioned (glass, trigger, etc.) are invisible. Who knows why?
You can use Textures \ Flush/Reload shaders to make them show up.
I also had problems with moving multiple selected patches. So I don't know the solution. If you have a brush selected too, and you grab that brush then you can move the patches without problem. This is not a solution just a workaround.