Act I Scene 1 - Zeffirelli 90

As for the Mel Gibson Hamlet, Zeffirelli sets it in an authentic Medieval castle, or rather, the ruins of one. Though the place must have been a lot more vibrant in its heyday, using the location pretty much as is gives us the rotten Denmark of the play.Prologue
This time, the story begins what must be two months hence, with Hamlet Sr.'s burial.
Instead of Horatio and the soldiers, the first characters we meet are the principals - Hamlet, Claudius, Gertrude and Polonius - four characters marked for death. It is thematically fitting that we first see them in a tomb. Mostly silent, the scene gives the actors the chance to present their characters physically. Hamlet is already a watcher. Claudius is imperious and domineering. Polonius is already noticing a problem with Hamlet's melancholy.
Gertrude is "all tears" as the play later tells us, but she also gives Claudius an odd look. Does she suspect? Not according to later scenes. Is it guilt from perhaps an affair she's been having with her husband's obviously younger brother? The play does infer a relationship there, with Hamlet Sr. off to the wars a good part of the time (not that we hear much about this in this version) and the hasty marriage. Or is it simply a response to his own look of "MINE, ALL MINE!" that makes her realize she must make a political move if she is to survive?

This prologue does borrow a few lines from later in the play. "Think of us as of a father..." stating very early on that Hamlet is next in line. It works as the first line of the play, presenting us at once with the story of a lost and replaced father, and the idea that Hamlet's own rise to power has been momentarily usurped. In effect, not only has Claudius replaced Hamlet Sr., but he's also taken Hamlet Jr.'s place.

I'll discuss the casting when these characters get a proper scene.

And Act 1 Scene 1?
Completely cut from the film. We do not meet Horatio and the soldiers until the end of Scene 2 when they come to tell Hamlet of the previous night's apparition. A natural cut since the scene is recounted anyway, but it does remove some elements from the play. Once again, we have an apolitical Denmark that doesn't necessarily seem unstable, and Horatio's role is cut down terribly, so there's little to learn about Hamlet's attitude through him.