One dramatic surprise is the death of Polonius. Polonius died simply by happenstance (or one could say because of his spying nature). (act 3 scene 4).
Another dramatic surprise is that Hamlet doesn't kill Claudius when he has the chance. With all his anger that he professes, he has an opportunity to kill Claudius and he doesn't. That tells us about Hamlet's character. He doesn't have the nerve to kill Claudius yet. (Act 3 scene 3)
Finally, Hamlet's conversation with his mother and the appearance of the Ghost is the final dramatic surprise. Although Hamlet says going into his mother's chambers that he is going to be kind, he really is harsh to her. He says, "A murderer and a villain, / A slave that is not twentieth part the tithe / Of your precedent lord, a vice of kings, / A cutpurse of the empire and the rule." He convinces Gertrude of her guilt, and she begs him to stop.
Then the ghost appears to tell Hamlet to comfort his mother, everytime the ghost appears it is unexpected, and thusly, a dramatic surprise. (act 3 scene 4)