Does anyone have a checklist or process to qualify an Electrical Worker?

See ANSI/IEEE C2 (NESC). They've been at it longer and have a much better working description.

Way too vague of a question.
A worker who does only residential wiring?
A commercial electrician that does only maintenance and hasn't pulled anything larger than #10, for years?
An industrial worker that spends 100% of the time involved with control circuits and machine control, where 120V is high voltage?
A construction electrician that installs miles of MV conductors, but hasn't ever actually energized a circuit?

An operator who knows very little about breakers and electricity. They give us a couple of hours of training and say go do it.

Go do what???
install breakers, operate them, do wiring, lock out/tag out?
We need more specifics about what you are inquiring about?
Go to OSHA's website and do a search for "qualified electrical worker" and you will find what OSHA considers qualified.
The NESC that PaulEngr mentioned applies to electrical utility workers.

What exactly is their job description? Quite a few years ago I worked as a Service Manager for an electrical contractor and there was a wide range of employees there from apprentices to control panel builders. I personally gave a test before I would hire anyone.

But according to 29CFR 1910.399:

Qualified person. One who has received training in and has demonstrated skills and knowledge in the construction and operation of electric equipment and installations and the hazards involved.

Note 1 to the definition of "qualified person:" Whether an employee is considered to be a "qualified person" will depend upon various circumstances in the workplace. For example, it is possible and, in fact, likely for an individual to be considered "qualified" with regard to certain equipment in the workplace, but "unqualified" as to other equipment. (See 1910.332(b)(3) for training requirements that specifically apply to qualified persons.)

Note 2 to the definition of "qualified person:" An employee who is undergoing on-the-job training and who, in the course of such training, has demonstrated an ability to perform duties safely at his or her level of training and who is under the direct supervision of a qualified person is considered to be a qualified person for the performance of those duties.

There is a lot of confusion where I work on this. The key is to read the training requirements for 'qualified' personnel. The definition is so vague that you can aggressively consider almost anyone qualified until you see the training requirement which clears up the question.