The main concern with nanoparticles is that they are so tiny that they are absorbed into the skin more than we want them (ideally sunscreen should remain on the surface of the skin). Once absorbed they might form unwanted complexes with proteins and they might promote the formation of evil free radicals. But do not panic, these are concerns under investigation. A 2009 review article about the safety of nanoparticles summarizes this, to date, in-vivo and in-vitro studies have not demonstrated percutaneous penetration of nanosized particles in titanium dioxide and zinc oxide sunscreens. The English translation is, so far it looks like sunscreens with nanoparticles do stay on the surface of the skin where they should be.  

An inorganic chemical, titanium dioxide is used as a dye to help products achieve a certain appearance, including whitening a product. Some experts and publications have described it as being akin to a paint primer that's used before the color is added to food in order to give products a uniform shine. Its presence is common in many items beyond Skittles including coffee creamers, cake mixes, and chewing gum. It's also used for pigment and in cosmetics manufacturing.

Lithopone 30% CAS No. 1345-05-7

According to a 2011 study published in Radiology and Oncology, titanium dioxide may lead to some adverse effects in the body, including oxidative stress, inflammation, and changes in cell signaling pathways. Additionally, pure titanium dioxide can be notably harmful when inhaled.