How to convert benzene to 1-bromo-3-iodobenzene?
It looks pretty good overall. The order of substitution is correct to achieve the required pattern but there are two points I would pick up on.


The final substitution of the diazonium salt is best done with $\ce{CuI}$ rather than $\ce{KI}$ as the copper(I) ions catalyse the reaction. Also heating is not required; the reaction can be run at room temperature (or possible slightly above but not much).
The diazonium salt is drawn incorrectly since it is ionic in nature. There is a triple bond between the nitrogens and a formal positive charge on the middle nitrogen, although in reality the charge is delocalised over both atoms: