How is the creature in Mary Shelley's Frankenstein morally ambiguous? What are some examples of that?

The creature that Victor Frankenstein creates in Shelley's Frankenstein is morally ambiguous because his narrative in the middle of the novel makes him sympathetic, but he is guilty of several violent acts. 

First, let's recall some of the creature's violent actions. The creature kills Victor's younger brother, William, who is only a child. He then frames the Frankenstein's maid, Justine Moritz, who is caring and innocent. He threatens Victor's life as well as that of his soon-to-be-wife, if Victor does not promise to make the creature a female companion. The creature does eventually kill Victor's wife, Elizabeth, on their wedding night. He also kills Victor's best friend, Clerval, and it could be said that Victor's beloved father dies of the grief caused by all of the other losses, an indirect result of the creature's actions (and Victor's actions, of course). From Victor's perspective, the creature terrorizes him and is an evil abomination. 

On the other hand, the creature's narrative, delivered to Victor (and the reader) at the center of the novel, makes him sympathetic. In the narrative, we learn about how Victor's actions have affected the creature, who is likened to an abandoned child. Victor, the father/creator, cast out his offspring/creation, and left him to fend for himself. The creature describes the agony of realizing that he is hideous and threatening to other people. He starts out with basically a good heart; he even tries to help save a drowning child. However, because of his ghastly appearance, people fear him and expect him to do evil. The creature maintains hope, though, and goes on to idolize and learn from the DeLacey family. He learns language and is able to communicate his own story articulately in the novel as a result of his observation of the family; this allows him to make a case to the reader and Victor that could create sympathy for his plight. The creature believes that he can approach the father of the DeLacey family and ask for help or companionship because the father is blind and so does not judge him by his appearance. Unfortunately, other members of the family come in during the creature's encounter with the DeLacey father and are deathly afraid of the creature. This serves as a sort of last straw for the creature. He now must appeal to his creator for help. 

Further, the creature appears sympathetic through contrast with Victor, who is also morally ambiguous. Victor abandons the creature and refuses to perform any sort of parental duty toward him. Victor allows Justine to take the fall for William's murder even though he knows the creature committed the crime (he tries to protect himself, as he does not want to be exposed as having made this monster). When we see Victor's behavior, we understand how the creature feels as a result of Victor's cruel and irresponsible treatment. At the same time, both Victor and the creature take actions that are morally wrong (Victor in making the creature and the creature in murdering others to take revenge on Victor). This makes both characters morally ambiguous.