Duct tape can be a great staple to patch a number of things. There are certain items in your home that should not have duct tape as they pose a danger to both your family and your home.
Water and duct tape don't mix, plain and simple. Water will leak through, get to the surrounding wood or wall structure and begin to form mold. Make sure to call a qualified plumber if you ever notice leaks forming.
2. Gas Appliance Vents
The purpose of gas appliance vents is to move the combustion by products to the exterior of the home. Failure to do so can cause carbon monoxide to leak into the home causing illness or worse, death. If you have a leak in these vents, do not patch them with duct tape. Make sure to call a HVAC contractor to repair as necessary.
3. Dryer Vents
Duct tape collects lint, lint is a fire hazard. If you want to prevent fires from starting in your walls, crawlspace or basement, then avoid securing your dryer vent with duct tape.
Duct tape despite it's name, should never be used on ducts. If there is a gap in the supply or return vents, make sure to use metal sleeves or mastic. Duct tape will eventually fail and does not make a good seal.
Devereaux Van Dyne, Certified Professional Home Inspector