I know how to clean the Master Files and have done so, but does anyone know if there is a need to clean the mods, too and if so, how so? Select the Master Files and the mod and go about the same process as I did for cleaning the Master Files? Or... Is it more complicated?

Select the mod you want cleaned, explicit dependencies will be automatically loaded along side of the mod. Implicit dependencies have to be selected to load with the mod. Go http://www.creationkit.com/TES5Edit_Cleaning_Guide_-_TES5Edit or http://www.creationkit.com/TES5Edit_Mod_Cleaning_Tutorial for a more detailed explanation.