I submit that the fact that you place "...and of course, some Freds are just screw-ups" last, as a sort of "oh, by the way", is what separates you from your questioner. It is easy to make Fred the exclusive scapegoat and to assume he's to blame and that the situation is likely that simple.

If every business debacle I've ever witnessed were a one-person screw-up, life would be ever so much simpler for managers.

I have always been guided by what I call the first rule of assessment, which was, I think, originally promulgated by master consultant Gerald Weinberg: "Things are the way they are because they got that way". Do not look first for a scapegoat, but for a systemic problem or oversight.

that is cool advice.

When I took a job as an administrator for a medical practice, my first major victory was to get the doctors to come yell at me rather than the staff. That way I could go out and see what the problem REALLY was.
90 plus percent of the time, the system was flawed. Fix the process and the problem went away. Yell at the person and the problem continues.
That said, some times the system was fine, the person was flawed in training or understanding or attitude.
The last one is the only one that got you fired.

In my experience, fixing a mess needs to come first. That's the part where Bob talks about "everyone's focus should be on what's needed to take care of it - nothing else."

Once you get the situation back on track, then you can start to look at causes, root analysis, responsible individuals, and so on. This discussion is much calmer, more professional, and less blame oriented when the original problem is under control.

The one thing this assumes is that problems are an exception. If your work environment is nothing but a problem, and has been that way for a while, then the "problem" is actually a whole order of magnitude (at least) greater than the immediate situation. In that case you'll probably have to tackle the job performance assessment first. Because it's likely the people who are causing the large and continuing issues, and you won't ever fix your problems until you tackle the personnel issues.

You can solve probems. You can search for the guilty, so that they can be punished. You cannot do both at the same time, because as soon as you start the blame game, everybody ceases to work on solving the problem and starts to do CYA and finger-pointing.

No employee works in a vacuum. Everyone has a supervisor, so an obvious question should always be "where's the supervisor?

The supervisor, if he or she is competent at that task, should be planning upcoming work, observing work in progress, keeping an eye out for problems, and providing "compass heading checks".

Sure, you're going to have the occassional situation where someone falls flat on their face; it happens with human beings. In my experience, each of your staff people will fall flat on their face about once every few months, to one degree or another, just because of the pace of work or changes in the work environment.

At the same time, very few people I've supervised over the last 30 years came to work every day with the attitude of "I'm going to make a mistake today." Sometimes you need to provide more training, more detailed instructions, a reassignment to another position or mentoring on finding a position more in line with their skills and education.

One aspect not discussed is what about the employee who's an innovator, always looking for a new way to do things, a changed approach that produces measurable improvements or applying a new process and technology? That person is going to make mistakes simply because he or she is pushing the envelope of the routine. Are you going to fire that person when something goes wrong? If so, you need to be fired because you're the impediment to improvements in the organization.