Can I use Regular Dish Soap in my Dishwasher?

This is a frequently asked question, either before trying liquid dish soap or after using it out of desperation when the supply of dishwasher detergent has run out. Dishwasher detergent and liquid dish soap are formulated for two very different types of cleaning. For the answer to this common question, read more in my Can I use Regular Dish Soap in my Dishwasher?