I can only talk about the teams I have worked in/run.
99% of complaints are candidates p*ssed off with the decision on their application where they have been unsuccessful. To put it into its extreme context, I was once stalked by a candidate who wouldn’t take no for an answer. They usually have no grounds for the complaint and their application. You have to remember the vast majority of people who apply are going to be rejected, so most complaints centre around this.
I am struggling to think of any “legitimate” concerns that were down to the process - but maybe I have just been lucky/ran a good ship

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I have had complaints about individual interviewers and they have been either taken off interview panels or have been retrained.
I have had complaints about how unnecessary assessments are (usually when people fail them) and then you just go through the legitimate reasons as to why those assessments are valid/reliable.
You get a lot of complaints about the lack of feedback, and then you have to explain you haven’t got time to do this as you’d need someone full-time just giving feedback to individuals for 7-8 weeks just for applications alone.
Grad Rec/HR don’t just make up these recruitment processes on the back of an envelope. They are usually thought through and professionally designed systems that have been tested/piloted and found to be successful. There is a lot of work put in to adapting and amending them when evidence suggests they could be better.