Fixing incongruities in PES Scan I tried to parameterize a particular x-y-z-t dihedral angle of novel molecule using a Quantum Mechanical scan, but I got the strange result below. 


The energy changes sharply around 130° and $E_\text{dihedral}(0°) \neq E_{dihedral}(360°)$.
I performed PES scan in gaussian09 and psi4 and I got the same results in different softwares.

I'm uncertain what approach to take to fix the scan. I saw some parameterization articles which didn't perform PES scan 0-360 degree. Other authors performed scan in the range of 0-60 degree or 0-120 degree and I didn't predict I will face a result like this. What is going wrong with my scan and how can I fix the issue? Would performing single point energy for each angle instead of PES scan help?
Even without seeing your molecule, I can say the referee is very likely correct. If you think of doing a scan of the dihedral of hydrogen peroxide, by symmetry the path from $\theta=180\to360$ should just be the reverse of $\theta=0\to180$. In your case, I don't know the symmetry around the dihedral, but at a bare minimum the energy should be the same after a $360$ degree rotation. The fact that it isn't suggests that some scan step (probably that point around $130$) irreparably distorted the molecule geometry so that additional steps didn't bring it back towards the initial geometry.

Generating the scan point by point may help, but you still have to ensure the rotations you are making are physical and aren't distorting the molecule too much. Sharp changes in the energy between steps are a sign that something is going wrong. 

You don't mention this detail in your question, but its also important to consider whether what you want is a rigid scan (where you just change this angle) or a relaxed scan (where you change this angle and then allow the rest of the structure to relax).