Degree Of freedom Of A Critical point
There are 3 phases at the critical point. Sub-critical vapour, Sub-critical liquid and critical fluid. 3 phases -> DoF = 0

That is one way to see it - and for convenience that is how I see it. It might be a bit wobbly to regard that as rigorous analyse though.

You can also say, more rigorously, that there is 1 phase and 2 constraints:
$$\left(\frac{\partial\rho}{\partial V}\right)_T = 0 $$ 
$$\left(\frac{\partial^2\rho}{\partial V^2}\right)_T = 0 $$ 
Subtract the number of constraints from the DoF and you get 0 again.

This defines a single point on the P/T curve.