One idea that I have is to speak with members of the community who are parents with small children, and ask them to share a recommendation, if they feel that they have had a very positive experience with their pediatrician, or if not, ask for the flags.
As far as warning signs go, I can only speak from personal experience, but some flags that got set off for me on our first pediatrician try were:
Young, unprofessional staff - The doctor's office seemed to be full of 15 year old assistants, who were doing everything from weighing our child to preparing vaccines. To make it worse, they often did their tasks incorrectly. An example encounter would consist of assistant weighing, doctor coming in, looking at charts gasping and exclaiming "Oh, he lost so much weight," then looking confused, going to reweigh our child, and finding out that the assistant did not know how to read the scale at all, and then explaining, in front of us, how she should read the scale. Repeat for multiple appointments.
Lacking a sense of doctor really caring (being impersonal) - Check for flag if doctor treats your child like an inanimate object instead of human. If you can instead discern passion and caring, it may be a good sign.
Not sharing thoughts - This may not be for everyone, but I want to know what is going on! Prying doctors in my experience can painful, so if you stumble upon one who is eager to let you know what they really think, it may be a good sign.
Musty office and/or doesn't look that clean - Huge flag to me, easy to spot right away. On the flip side, if both the space and the doctor are very well maintained, it may be a good sign.
In evaluating, I would attempt to gauge the 'space as a whole', as well as the doctor, but honestly, it is a difficult thing for us laymen to do on the fly. Luckily med school is pretty hard, so I would imagine most pediatricians know their stuff. Trusting this, I'll look a lot at how much I liked them as a person.
If they came across to me as genuine, intelligent, passionate, caring, friendly individuals who loved what they were doing, it would be a good sign for me.