My main rule for this is no hindsight bias. Dan Mullen was bad this year, but that's "hindsight bias." RichRod flopped at Michigan, but he seemed like a good hire based on his record at West Virginia. I think the "worst hires" are the ones that should've been obvious the moment they were hired.
Derek Dooley, Tennessee. He was 17-20 at Louisiana Tech. Even if you find a good G5 coach they aren't always success at the P5 level (see Justin Fuente), but Dooley was a bad G5 coach, whose only marketable credientials were that he was Vince Dooley's son and he once worked for Saban. As we all know, he was a disaster in Knoxville and probably the worst recruiter at UT in the past 3 decades. Left the cupboard completely bare when he left.
Paul Hackett, USC. He was a bad coach at Pitt. He was the OC at Kansas City for a few years and USC decided he would make a great coach. He didn't. The one thing you can say in his favor ... he did recruit well. Pete Carroll inherited a loaded roster from him, so he wasn't disastrous as some hires, but he was a terrible HC.
Bill Callahan, Nebraska. There haven't been a lot of NFL-to-college success stories, but Callahan was an NFL-to-college nightmare story. He was not a good NFL coach; and his record was inflated due to inheriting a loaded Oakland Raiders team. But he was fired primarily because of how toxic of a personality he had. So Nebraska decided they needed him as their Head Coach. He then proceeded to go 27-22. This was back when Nebraska was still considered a top program. Callahan started their decline.
Gerry Dinardo, LSU. He went 19-25 at Vanderbilt so LSU decided he'd make an excellent hire. He went 32-24-1, but he was 6-15 in his final 2 seasons. If you can't win at LSU with all the talent in Louisiana, you can't be a very good coach. It basically took Nick Saban about 2 days to turn around Dinardo's trainwreck and he won the SEC 2 years later.
Jon Embree, Colorado. He was a Colorado alum and that's the only conceivable reason I can see that he got the job. He was never a Head Coach or even a coordinator before he was offered the job. He lasted 2 years and went 4-21.
Derek Dooley was a really poor recruiter. He covered it with some talent from the Kiffin year.