Does the butler actually clean anything that needs to be cleaned?

In households having staff as elevated as Butlers, there are usually also maids, gardeners and cooks. Butlers often serve as "supervisors" of larger staff and that's why you see the Butler checking for dust every so often. In this case, it seems the devs made Butlers in the very same fashion. If you want a staff person to clean, that would be a maid.