Here's a few things I've noted:
- Cavern of Souls actually makes creatures of the chosen creature type uncounterable
...Except if you have the use the colorless mana to cast the creature (say you want to cast a Thought-Knot Seer off 2 Plains, a Mox Emerald and a Cavern naming Eldrazi; you will have to use the colorless mana from Cavern, thus TKS can be countered).
But only if you have to. If you don't have to (ie, you're also using another colorless source), you're assumed to be using colored mana for the generic mana portion of the cost, regardless of whether you announced it. [Source]