Are peppers on the same plant genetically identical?
Also, what is a hot pepper phenotype? What makes a phenotype a phenotype? 


Phenotypes are the quantitative or qualitative characteristics that arise from the interaction of an organism's genetics with the environment.  For pepper plants, height is a phenotype, as are leaf color, average fruit weight, and pretty much every other characteristic you can measure. Capsaicin concentration (mass of capsaicin per unit mass of fruit) is a phenotype that is relevant to hot pepper enthusiasts.  


  What causes significant variation of pod shape and size on the same plant? Environmental factors? Genotype/genetic factors?


It's hard to know.  There could be a genetic component that results in inequitable distribution of resources to individual fruits during plant development. There could be environmental factors that determine why one fruit is larger than another -- perhaps the larger fruit developed during a time when water and sunlight were plentiful to the plant.


  Are peppers on the same plant genetically identical?


See this excellent answer given by mgkrebbs to the question Are the seeds in a single capsicum fruit genetically identical?