The "rate of change of theta" should indeed be written as "radians per second," not "radius" nor "radii" per second. Theta is an angular measurement, whereas "radius" is a length, and it makes no sense to talk about the change of theta per unit time as a length. So bottom line is- it's a typo. As for the circumfrential velocity - you calculate that as rate of change of theta times the distance from the origin at that point in time: