Why are dim peaks usually so wide? Does this mean the dye distribution is more heterogenous within these beads?

Wider dim peaks are partially due to an instrumental artifact called the photoelectron statistical error. Essentially this is counting/conversion error in the PMT (the instrument detects x amount of photons for which it’s supposed to create y amount of electron output signal, but sometimes it miscounts the photons creating false electron signals). The error rate is fixed, meaning it will happen every X photons (it’s a very low error event), thus this counting error has a lower standard deviation at higher counting events (the more photons you convert the less the error impacts the results, i.e. brighter signals suffer less from the error), leading to lower fluorescence CVs for more intense signals. All of this is a wordy way of saying that dimmer peaks are more broad partially due to the instrumental error, relative to more intense peaks.

Credit to Excyte Cytometry, Click to read more.