Safety
While "black lights" do produce light in the UV range, their spectrum is confined to the longwave UVA region. UVA is considered the safest of the three spectra of UV light. It is the higher energy (shortwave) light in the UVB and UVC range that is responsible for the DNA damage that leads to skin cancer. UVA light is much lower in energy and does not cause sunburn. UVA is capable of causing damage to collagen fibers, so it does have the potential to accelerate skin aging and cause wrinkles. UVA can also destroy vitamin A in the skin.
UVA light can cause DNA damage, but not directly like UVB and UVC. Due to its longer wavelength it is absorbed less and reaches deeper skin layers (the leather skin), where it produces reactive chemical intermediates, such as hydroxyl and oxygen radicals, which in turn can damage DNA and is a high melanoma (a dangerous skin cancer) risk. The strength of a black light in comparison to sunlight is minuscule, so it is doubtful that UVA light poses any significant health risks. The weak output of black lights should not cause DNA damage or cellular mutations the way sunlight can.