I was called to examine an enormous fish kill in Chesapeake Bay, but could not determine the cause. Then just four years ago a similar fish kill in the same bay was found to be due to Pfiesteria about which we knew nothing a decade earlier. Not sure I'd like to go back to study it after hearing what its toxins do to the nervous system and memory. I had some health problems of an indefinable nature, but never associated them with several weeks of looking over plankton and dead fish. News reports simplistically call it an alga, which bothers me as a biologist.
Definition depends upon one's perception and background.
I used to place dinoflagellates together with other protozoan phytoflagellates, and still would do so, except now under the umbrella of being a protist rather than a plant or animal. I think calling Pfiesteria an alga diverts or diminishes public attention from this frightening thing, for people tend to say, Oh, it's only a plant and we certainly can do something about that. Well, no, we can't. It is a life form we do not understand at all. So, Dave and Mol, by all means continue to call attention to this strange and worrisome organism, whatever it is called.