A non-linear gain for VCO is acceptable as long as it is monotonic (If you look for linear VCO much better than you currently have, you may never end your design phase). It is the non-linearity of PFD that can cause noise components to fold in to your spectrum.
Your PFD transfer curve is not monotonic, which can cause serious problems that your PLL may never lock if there is large enough phase difference to start with.
In the linear region it looks very linear (if you had sufficient points in between), so that should not be in your list of your problems. If you are not designing a fractional-N PLL, the PFD linearity requirement would be more relaxed (but slope changes are not allowed)
Just fix the phase of one input and sweep the phase of the other input and look at the voltage at the CP node to plot the transfer curve