The digestive system's function is to break down food into molecules the body can use. The organs within the digestive tract carry out the digestive process. There are two ways that break down food into nutrients. There is mechanical which is chewing and chemical which are enzymes. The intestine is responsible for the absorption of nutrients in the blood to be delivered throughout the body.
Advantages of the digestive system for some animals are their ability to absorb nutrients by diffusion. For example, earthworms have a straight intestine so it's beneficial to them because they absorb nutrients by diffusion. Breaking down carbohydrates, protein and lipids are important because they help provide or store energy and build muscle and tissue. The stomach walls provide gastric juices that help kill off germs that enter the body. The liver is beneficial because it separates the good stuff and the waste. To maintain a good digestive system, you obviously need to have a healthy diet and exercise.
There aren't that many disadvantages for the digestive system. I think a disadvantage of a straight intestine is that it's harder to break things down. There are some problems that have to do with the intestines like irritable bowel syndrome, inflammatory bowel syndrome and cancer of the bowel.
Sources:
http://answers.yahoo.com/question/index?qid=20120602233022AAhePnf
http://visual.merriam-webster.com/human-being/anatomy/digestive-system.php
http://www.cyh.com/HealthTopics/HealthTopicDetailsKids.aspx?id=2727&np=152&p=335
Holt, Rinehart and Winston Modern Biology
Austin: Holt, Rinehart and Winston, 2002