Is it safe to use paper towel as a filter when brewing? Are there any chemicals or dyes in most common paper towels that would be harmful if I brewed my coffee using the towel as a filter?

If it is safe, will it affect the taste of the coffee at all?
Coffee filters are subject to food grade standards. They aren't just convenient shapes and stronger than paper towels, they have substantially less toxins i.e. bleach byproducts such dioxins (strong carcinogen). As well many paper towels have various purfumes, inks and other chemicals only GRAS (generally recognized as safe) for external use on your skin. Not as a filter medium for an ingested beverage.

And as for white being devoid of dyes and chemicals.. natural wood pulp which is what filters and paper towels are made of is a murky brownish grey colour at it's lightest. If it's white it's been bleached. And in most cases with a more potent bleaching agent if the intended use is for paper towels than filter media.

Sure you can use paper towels. Most brands won't burst suddenly and it won't kill you on the spot anymore than BPA in older water bottles or lead in drinking water. But is this where you want to save a few pennies - by using something that is going to bring unnecessary amounts of known carcinogens into your diet?

I'll stick to coffee filters myself. And unbleached (brown) ones at that.