The texture of paper towels tears easily on both high- and low-pile fabrics, being ripped apart by the fibers that comprise them and leaving remnants behind.
To clean carpets and rugs, blot the stain with white microfiber rags, sponges, or soft-bristled brushes. If all you have is paper towels, make sure to blot to minimize tearing.
Paper towels can potentially scratch and abrade electronic screens, leaving permanent marks and indentations on their interface as well as leaving lint behind.
If your screens need a wipe down, use microfiber cloths, diluted 70-percent isopropyl rubbing alcohol, electronic wipes, or a vacuum with a narrow nozzle attachment.
Paper towels are made with chlorine and formaldehyde, and many paper towel brands also contain Bisphenol A (BPA), which is thought to have negative effects.
There is no reason to subject yourself to possible health risks when you can air dry your items using a dish mat or rack. If you need to dry them faster, use a clean dish cloth.
Paper towels can easily be torn and ripped by the fibers in upholstery, leaving paper trails in the wake of your wiping, and often just rub a stain deeper into your furniture.