There are a number of problems that revolve around using multi-band compression. The timbre of the instruments in the mix can be greatly effected. Cymbals, vocals, and sometimes guitars tonal balance can be altered. Small phase issues also occur with any type of crossover network as well as EQ. It is also a tool that can very easily be abused and over used.
I use it for problem solving much like others in this topic. De-essing, LF control, and extreme dynamic issues are problems. In general, I agree with Mr.Blackwood, though. I prefer to avoid it unless needed. If your mix is sitting right frequency wise, you shouldn't need it. It does alter the sound of the mix in ways that we should not be altering the mix IMO.
OatBran