Is a microwave oven dangerous?
If there is no concern over the quality of the food, I'm guessing the question is more specific to whether the microwave oven is a safe piece of equipment to use.

The U.S. Food and Drug Administration says:


  Manufacturers must certify that their microwave ovens comply with strict FDA emission limits. The emission limits are well below the threshold for risk to public health.
  Most injuries related to microwave ovens are the result of serious thermal burns from hot containers, overheated foods, or exploding liquids.
  
  There have been extremely rare instances of radiation injury due to unusual circumstances or improper servicing.


If we're not talking about the oven itself, and rather the nature of chemicals involved with its use, then we could talk about microwaving with plastics with foods. There are sources online that raise concerns over plastics leeching dangerous chemicals into the food. 

Harvard School of Medicine says:


  
  If you’re concerned about plastic wraps or containers in the
  microwave, transfer food to glass or ceramic containers labeled for
  use in microwave ovens.
  Don’t let plastic wrap touch food during
  microwaving because it may melt. 
  Wax paper, kitchen parchment paper,
  white paper towels, or a domed container that fits over a plate or
  bowl are better alternatives. 
  Most takeout containers, water bottles,
  and plastic tubs or jars made to hold margarine, yogurt, whipped
  topping, and foods such as cream cheese, mayonnaise, and mustard are
  not microwave-safe. 
  Microwavable takeout dinner trays are formulated
  for one-time use only and will say so on the package. 
  Old, scratched,
  or cracked containers, or those that have been microwaved many times,
  may leach out more plasticizers. 
  Don’t microwave plastic storage bags
  or plastic bags from the grocery store. 
  Before microwaving food, be
  sure to vent the container: leave the lid ajar, or lift the edge of
  the cover.