As an academic physician myself, I've been thinking about this for some time.
There are many parts to this answer.
First, what makes a good physician? It's not all about being able to diagnose diseases, because let's face it, 95% of our practice is essentially "bread and butter". What you may think is difficult is what we do all day. A good physician is a good medical expert, but also a good communicator, collaborator, leader, health advocate, scholar and is professional (see CanMEDS framework). All this combined is a "good" physician.
Now, as others have pointed, seeing a subspecialist is better in some cases. Again, most issues can be dealt with by an "average" physician without problem.
For surgeons, there's a link between how frequent a procedure is performed and outcomes. If you need something "special", see a surgeon that does that procedure often. It doesn't guarantee a good outcome (one can do a crappy job often!) but there's a correlation.
For the complication risk, this can be a double edge sword. Highly skilled surgeons are often referred complicated cases at high risk of complication, so their numbers aren't good. The others get the "easy" cases so their numbers look better...
From my experience as a trainee, research "status" ie number of publications, talks, books chapters... don't correlate well with quality of care. They can be good at writing grants and papers, but when it comes to getting things done in the clinic, it's a different story.
As for physician review site - Yelp; well, that will give you mostly information of the physician's communication skills, which is a big part of our job, but probably not what you have in mind when trying to find "the best".
I'm a radiation oncologist specializing mostly in lung cancer and brain radiosurgery. Even I have a hard time judging the quality of the radiation therapy treatments decisions and parameters of my own colleagues (treating other sites). I can't imagine trying to find a "best" physician for a specific problem without my network and my background.
Thinking about it, I would follow your PCP's advice; who he-she knows, classmates... We know who the "good & smart guys" are. As I said above, it doesn't guarantee quality care, but it's a good start. If it's a really important problem, seeking a second opinion is usually the way to go. I would go to a tertiary care centre (university hospital) with a good reputation.