André Joyal has pointed out to me that there is an error in my Quillen model structure for 2-categories. I fix the error. Along the way, I describe a Quillen model structure for the category Bicats of bicategories and strict homomorphisms of bicategories. I also show that the canonical adjunction between Bicats and 2-Cat is a Quillen equivalence between the model categories.
This has been written up as a preprint of the same name.