What health risks come from a dirty turtle tank for my pet and me?

Thanks for your question about Nugget. For the human health part of your question, the biggest disease that we worry about passing from reptiles to humans is Salmonella. There are other bacteria that they can also carry, but they don’t seem to cause as many problems for humans as Salmonella does. I would recommend washing your hands thoroughly after handing Nugget or cleaning the enclosure to help with this, and to clean the area where you dump the water (ie if you use the sink).
For issues relating to a dirty enclosure for Nugget, there are many health problems that can occur with poor husbandry. They can get very sick from exposure to the high levels of bacteria present in their poop, and may stop eating, growing, etc. Often these infections take a long time to treat, and some reptiles don’t recover.
I hope that answers your questions, and thanks for using Petco Pet Education Center, formerly Petcoach.