Before you agree to do a job, do you first make sure the GC, or the guy in charge, knows what he's doing? Can he run a job?

I try to get as much info from them as I can. If they are a complete idiot I add to my number, if they are a homeowner doing the work and they don't sound like they know what they are doing I add to my number. Most of the time you will end up answering tons of questions from them because they are in over their head and time is money.

When I asked "can you do the job?", some referred to the problems caused by the GC's inability to schedule, or otherwise do 'his' part of the job.

Do we consider who the GC is, and his past performance/ reputation before committing to a job? Has anyone refused a job because of their lack of confidence in the builder?

In short, do we 'pre-qualify' the GC as well as the customer?

"In short, do we 'pre-qualify' the GC as well as the customer?"
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Yes

GC's will tend to take on jobs with conditions, that require additional work, and estimate it as standard construction, in these cases working with this GC will take you down with him, so we try to first make sure he knows what he's doing.

When I was getting started, I would work for just about anybody. Now, I'm a little more selective. A bad GC or a homeowner/self-contractor that doesn't know what they are doing can be a nightmare. These types can make a simple project take you 2 or 3 times as much labor as it should. The funny thing is they cause you to do extra work but act like you're the idiot for not automatically knowing that they wanted a 3 circuit whirlpool tub and a steam generator that draws 126 amps.