How does Shakespeare produce a memorable dramatic and linguistic effect in the opening scene of Hamlet?

This is a great question, because memory is one of the themes of this scene. The Ghost urges Hamlet to remember him, and Hamlet promises to do so. One of the key ways that Shakespeare makes this scene memorable is through repetition, which, after all, is one of the best ways to memorize something. For example, the Ghost repeats "swear" over and over, even though Marcellus and Horatio have already agreed to swear silence. This effect is both memorable and dramatic, since the repetition also increases the urgency of the Ghost's desire for secrecy and gets Hamlet even more worked up. Another line that uses repetition is "that one may smile, and smile, and be a villain." This line is very famous because it is insightful, but also because the repetition makes it memorable for an audience member or reader. Repetition is also an important linguistic tool, so you might seek out other instances of repetition in the scene to help you fulfill your assignment.