What problems do biologists have with the kingdom Protista?

Lynn Margulis and Karlene Schwartz, in their book The Five Kingdoms (W. H. Freeman, 1998), struggled heroically to justify the Protista (they preferred the term Protoctista) kingdom. "Undulipodia (aka flagella) were present in common ancestors to all the phyla, even before mitochondria, given that the anaerobic archaeprotists bear them." However, a sentence later they admit that "in some phyla, all members bear undulipodia, in other phyla, they are absent ... " It seems a shaky foundation on which to build a kingdom. All human cells are fathered ultimately by sperm, which bear undulipodia, but no one has suggested that humans are therefore protists.