Some of the most significant features of this scene are the setting and atmosphere around Hamlet. The swirling, raging waters certainly reflect Hamlet's state of mind as we reach this point in the story. He knows that he should do, but recongizes his lack of action -- hence the "dream-like" feel that the previous post mentions. I also notice the camera work in this scene -- close -ups of Hamlet's head -- keeping the audience connected to the fact that these are Hamlet's thoughts, not a speech he is giving to someone else. He is also in the same or a physically similar place as he was when he encountered the Ghost, so there is that cue to the audience about what this is all about. He is in a cold, isolated, desolate place that even feels a bit sinister and dangerous. This is all in keeping with the mental and emotional turmoil Hamlet feels.
Olivier's Hamlet seems to be in a mental fog throughout the whole speech. That's no doubt why it was filmed in fog high above an angry sea. Moreover, he acts at least half asleep and rather depressed. The only real animation he shows is when he delivers the line, "...perchance to dream." It is at that very moment that, having already dreamily taken out is dagger, he acts as if he's just awakened, startled, from his reverie. But even then, relatively awake, he is listless and contemplative. He carelessly drops the dagger into the sea, and it disappears, as he soon does, into the mist.
The entire sequence is played as a dream within a dream, where nothing happens but in the mind.