Bacteria
In 2001, the Journal of the American Dietetic Association released documentation showing that dish towels can contain harmful bacteria. The towels can pick up bacteria on peoples' hands and on unclean dishes. When left wet, the towel becomes a breeding ground for bacteria, and the next time you use it to dry dishes, it transfers the bacteria to your dishes. The Food and Drug Administration requires that public kitchens must air-dry their dishes, rather than use dish towels.
Grip
When you dry dishes with towels, you're picking up wet wishes and using a towel that gets wet. This combination can make handling dishes difficult, and a dish can easily slip out of your hands and break on the floor. A dish that doesn't get fully cleaned may contain soap residue, which will make it even more slippery.
Mixed-up Towels
Some people don't differentiate between hand towels and dish towels, which can have serious bacteria repercussions. If you don't wash your hands with enough soap and for a long enough duration to kill all the bacteria, you will transfer those germs to the towel you use to dry your hands. If you use that same towel to dry your dishes, you're adding that bacteria to your plates, glasses and cutlery.
Considerations
If you find that using a dish towel is ideal for your situation, make sure to use a clean, fresh dish towel every time you dry a load of dishes. When you're finished with the load, add the dish towel to a white load of laundry and add bleach to ensure you kill any bacteria. Using a different dish towel each time you wash dishes may result in extra laundry duties, but it will keep bacteria off your dishes.