The Crowd client (or possibly Crowd itself) automatically normalizes user/group names to all-lowercase before handing them off to the consuming application. Hudson seems to be using case-sensitive matching for authorization of groups.
The result of this is that if you enter a group name with upper-case characters in it, in (say) the matrix-based authorization form, Hudson won't grant correct authorization to members of that group, because the name of the group won't match. If you enter the same group name as all lower-case, it will work fine.
I'm not sure yet whether it is possible to work around this in the plugin...