I have adopted two parrots off of Craig's List. Both I think were successful - although my latest is a bit of a challenge as I've discovered he has a handicap.
That said, I will give you advice and things I learned while perusing CL.
There are A LOT of bird 'flippers' on Craig's List. Generally, you will see them have multiple postings sequentially - you can tell its the same person by:
1. The same crappy picture quality - terrible picture of the bird. Someone that owned and loved their bird will more than likely have good quality pictures - I mean don't we all have 1,000s of pictures on our cell phones of our fids to show anyone that wants to see? Or is that just me?
2. They generally write very short descriptions, poor or no punctuation, and poor grammar. Example: "two cocktails rehome fee 200 obo no cage" (Yes... COCKTAILS - just saw this one the other day).
3. They try to get as much as or close to the same price you would get from a breeder... which is just SILLY.
Typically, people that genuinely care for their animal and want to find it a good home will not be charging an astronomical fee, and they will give a good description of the bird, and why they need to find it a home.
The questions I always asked are:
Why they need to rehome the bird. How old the bird is. What is the bird's current health condition. Is the bird tame. What is the bird's personality.
I also think it is important to "meet" the bird first, making it clear to the owner that you aren't definitely purchasing YET. That way you can get a good idea of the bird's living situation, and if this person was taking good care of the bird or not. If they refuse to have you into their home and will only meet at a local gas station... that's a bit sketchy to me!
Hope this helps!