What is the purpose of vent holes in stovepipe?
I always assumed this allows extra air to be drawn into the flue to insure oxidation of any CO to CO2. These holes would also by bringing in more air increase the back pressure and so lower the air draw at the burner into the optimum range.

I know the flue on the old gas tank water heaters was fitted with a "draft hood" designed to take in extra air at the top of the tank / bottom of the flue. It seems to be that if not designed correctly this opening could allow escape of combustion gasses out these holes, but I guess the openings generally work as intended.

This video asserts that the purpose of the vent hood is to prevent downdrafts from wind blowing over and into the vent on the roof from extinguishing the gas flame. 

My 13-year-old Bosch tankless water heater (natural gas fired) does not have visible openings at the bottom of the flue. It is a "first generation" model with a standing pilot light and without a power vent.

My 26-year-old Carrier natural gas furnace likewise does not have these holes but it has a power vent on the exhaust flue.