Why is mammal coloration so dull?
I don't think, there is a precise answer about the evolutionary mechanisms, but "mechanically":


mammals have principally just two types of pigments: eumelanin and pheomelanin, both of which have their color variants, but within a known range. Bird pigments, besides melanins, include carotenoids and porphyrins. Arthropods generally have carotenoids, melanins and ommochromes [and other pigments?]. E.g. carotenoids and ommochromes alone can create rather "exotic" coloration from a mammal point of view (green, pink, violet).
both birds and insects actively utilize iridescence. With fur it seems to be technically much more difficult to achieve than with feather or scales.
many (most?) mammals do not differentiate colors. Birds have much better vision abilities in this respect. From a selectionist point of view this cuts out a considerable part of selection acting upon coloration, which could otherwise produce broader spectrum of phenotypes.