Multi-nucleated cells: advantages and examples?
Muscle cells are the only cells I know of that are polynuclear. With respect to monocytes, a concise review of their nomenclature can be found in this paper by L Ziegler-Heitbrock, P Ancuta, S Crowe, et al. (Blood, 2010). Apparently it has had quite a complex and confused biochemical characterization, but the article states the name indeed derived from its single lobed, mononuclear morphology. This is in distinction to other phagocytes which have multi-lobular nuclei (polymorphonuclear cells).

With respect to advantages, a multinucleated cell makes sense when the speed of intracellular signalling is important (e.g., calcium diffusion). It may also be useful in the case of cells when the cell needs to coordinate the synthesis of large amounts of protein.