The calorimeters were built to have good position and energy resolution. The position resolution is needed, of course, for the precise determination of the acceptance of the calorimeter; the energy resolution is needed to distinguish true Bhabha events from the off-momentum beam particles which contribute to the background.
You can read a discussion of the construction of the calorimeter (with lots of pictures) which describes how the calorimeter was built to achieve these goals, and a discussion of the quality of the data that was taken (also with lots of pictures).
Information about the luminosity monitors
Information about the forward detector