When the clues are missing, it cannot be resolved. Such are the cases of John F. Kennedy and the young Jon Benet Ramsey. There was not enough clues or evidence to form a proven conclusion, and so their cases were left open. There is a television show called Unsolved Mysteries that covers a plethora of these types of cases. Unfortunately, the unsolved variety of mystery is inconclusive by its very nature, and it leaves you with no sense of closure or finality.
Plot twists add interest to any mystery.
They shock the viewer or reader, and cause the audience to think more and consider new elements that perhaps they had not thought of before. The Sixth Sense is a prime example. Throughout the movie you watch a psychologist and his patient, a young boy who, in his own words, sees dead people. Some mysteries have indefinite endings they are inconclusive. Like the open murder cases mentioned before of JFK and Jon Benet, or maybe some other example where a mysterious happening is in the end attributed to natural phenomena or even wildlife instead of the human or super-human cause you were led to believe in.