Sourdough Starter Black Spots
I would discard this batch, carefully clean everything and start over.

If you truly mixed well in the beginning, then the fluffy bits are probably mold and the black spots are somewhat fishy as well. After only 24 hours, you won’t have a strong culture going under that top layer and the mold problem will likely continue. Remember that a sourdough means that the desired yeasts and bacteria grew faster than the unwanted ones and that they create an environment where they can outcompete possible intruders. While a mature starter with problems can be salvaged by using just a bit from an unaffected area, this is not true for fresh flour and water mixes. 

If you start over now, you won’t have lost much: a day and a cup of flour perhaps? 

Not part of your question but perhaps helpful:
The amount of yeasts is greatest on wholegrain flour - it may be worth it to get a small bag from your local organic store. For upkeep / later feeding, white flour is fine.