Create a group and also create actions to activate or deactivate that group.
If you try to change the action to a group that doesn't exist an error is generated, which is as it should be.
However, if you change the name of the group, the actions are not changed to correspond to the new name, so you can end up with a situation where you are trying to activate or deactivate a group that doesn't exist, with sometimes amusing results.
GroupNameBug.capx demonstrates the problem. Run it and sprite is created on touch. Now try changing the name of the group. The actions are not changed, and when you run the behavior is quite different from before.
While this is counter to C2's normally excellent consistency checking, I would rank it fairly low priority in the general scheme of things since, even though you can get some strange behaviors as a result, you don't actually lose anything other than time (or possibly your mind. )