As frequently happens, Zeffirelli chooses to infer a lot of what's being said rather than use the dialog, but the net effect is to deny the audience insight into Claudius' character. Rosencrantz & Guildenstern's role in the sequence is entirely, cut as is Polonius announcing his plan, but this is par for the course for a trimmer Hamlet. Where we lose the most is in Claudius' confession. He finds himself in the chapel, crossing himself before a tapestry of the crucifixion, directly(?) from his emotional outburst at the play. The scene picks up at "My offenses rank" and doesn't get much farther than "a brother's murder" before he kneels and prays silently. It's enough to show his guilt, but not enough make us empathize with his situation. There is no internal debate about the impossibility of his redemption, and most egregious of all, the final line about words without thoughts has been excised. As Hamlet does his thing from the doorway, Claudius at times sobs loudly, and croaks out parts of his speech in prayer ("wretched state" etc.), so this King feels very guilty indeed. However, we're left believing he might yet be redeemed, or that he at least thinks he can be. So Hamlet is right to stay his hand, and the scene's irony is completely lost.

A great disappointment.

Claudius is a man upset by Hamlet's play, and struggling to keep his emotions in check. He's not just enraged, but guilt-ridden as well, making for a scene with Rosencrantz & Guildenstern that's more emotional and intimate than most. Here, Rosencrantz's speech about the realm empathizing with its King becomes a way of consoling Claudius, and he even feigns(?) being moved, makes his voice tremble, etc. The sycophancy works and Rosencrantz gets a manly embrace from the King. Often painted as irrelevant cogs in the courtly machine, the R&G of this version seem to be in better graces, at least at the moment. This fits within its theme of Claudius preferring (and showing fatherly affection) to every young man BUT Hamlet, though he may simply be in a sort of daze, acting automatically. Indeed, when Polonius comes in, he gets no reaction. By the time the King breaks with his daydream and answers, Polonius has already rushed off. And then there is a sudden explosion of emotion, a sneeze as much as a sob, and though alone, Claudius still tries to maintain his facade.

Patrick Stewart gives his lines a strong measure of sarcasm to make Claudius reject his own capacity to be forgiven, and this is something that's quite important to the Medieval point of view - the idea that the King is the voice of God, the head of the stately body and true origin of the realm's welfare. We've seen how this is true of Hamlet's Denmark, a weakened and corrupted country, and it's in his role as God of Denmark that Claudius rejects his own salvation. His damned state is of his own making, and at the very end, his final line is a full acceptance of his evil and damned state. It doesn't matter what he does to repent, his fate has been sealed, and so he may give in to evil since once damned is thrice damned. It's not that he rejects divinity, quite the opposite, it's that he sees himself as forever unworthy of divine grace. His later "sin will pluck on sin" is less an observation than justification for his wrong-doing.
From his desk, Claudius forces himself to a small altar to pray, every move an effort, and Hamlet comes upon this scene by accident. Unlike the close calls of other adaptations where Hamlet gets quite close to Claudius, here he never even crosses the threshold. The soliloquy is spoken directly to the camera, which gives Jacobi's Hamlet an opportunity to explain himself. It's the audience that doesn't understand this particular delay when Hamlet has just vowed to finally act, and he feels compelled to justify his non-action. It's no harder to reconcile than his apparent relish at describing the compromising positions he might catch the King in, including everything he hates about him, such as his "incestuous bed". Regardless of how it is played, the text itself is contradictory in this. Hamlet at once WANTS to catch his stepfather in bed with his mother, and then expressly FORBIDS his mother from sleeping with him. But that's Hamlet's own wretched state, balanced between putting a stop to Elsinore's evils and maintaining them to fuel his self-pity. He knows who he is now, but who will he be when it's all been said and done?

As usual, Olivier tells us more with his staging than he does with his actors' performances, which makes up for his large cuts to Shakespeare's lines. Obviously, the largest cut where this sequence is concerned is the elimination of Rosencrantz & Guildenstern, but their scene here is easy to excise. Instead, Polonius runs to Claudius directly with his plan. He has to seek him out because the King has been sitting alone in darkness since the Mouse-Trap, and strangely for him, crownless. As we discover him, his face is completely in darkness, an image of his sin, yes, but also of a man devoured by guilt. He does not face us out of shame. This Claudius seems more repentant than others, in tears, kneeling without his words prompting him to do so. The camera focuses on his hand for a long time, another clue that it is very much the Ghost's eye-view in this adaptation. A Ghost fixating on the hand that murdered it in life.

Hamlet stumbles upon this scene, walking behind Claudius and only barely noticing him there. His speech is in voice-over to avoid the theatricality of words spoken and unheard. In many adaptations, Hamlet's presence in this room feels deliberate. A crime of opportunity to be sure, but it ties into his last speech. He is ready to do anything, and welcomes this chance (until he thinks about it some more). In the way Olivier stages it, Hamlet is taken by surprise by this opportunity, and feels a sudden rush to avenge his father, but it's all going too fast. It makes his decision not to go through with it more realistic, where a slow or thoughtful approach would infer more time to think about acting to counter the time to think about NOT acting.
The statue of Jesus in this scene is no casual set dressing. Olivier uses it in his staging to give Hamlet pause. It's in seeing it that Hamlet makes the realization that Claudius should not be killed a-praying, and Jesus becomes a character in the room, silently looking at the characters, his eye line able to meet theirs, and a voiceless conversation does occur! In this praying scene, prayers are answered, not by some divine mechanic, but by characters hearing themselves speak and reacting to it (Shakespeare's great gift to literary characters, according to critic Harold Bloom). Divine inspiration and wisdom coming from inside the characters. As Claudius' words "don't rise up", the imagery and this more secular reading tell us different, and that - a double irony - Christ does forgive him, but he cannot forgive himself. The last line sees the camera drop down, obscuring Jesus' face and moving down a dark slab towards a sobbing Claudius.

There's some small shuffling of scenes in this section, as the first part of the scene - Claudius and his various sycophants - is placed before Hamlet's short soliloquy technically part of the previous scene, before resuming with the Claudius' confession, an edit that creates more tension by putting Hamlet's "I'm ready" speech right up close to his opportunity to show he is. In the sequence preceding, Claudius is seething from Hamlet's affront at the play, and is putting into motion Hamlet's exile to England. Rosencrantz & Guildenstern are also assigned to this voyage, which immediately makes them worry that they're sharing in the punishment. This is the scene where they try to understand if they've fallen out of favor or not. At least, that's how it's played in this adaptation. As Claudius ignores the two gnats, R&G give each other looks and try to glean some kind of response from the King. There's a sense that they realize they are a "noyance", but can't get out of this conversation. When Claudius, lost in murderous thought, snaps back to reality, it's like they never said a thing. He's back on the question of the exile. Had he listened, he might have heard a warning about the relationship between King and State, his Denmark about to fall because he has. That general groan is merely delayed, the King and corrupted State's days prolonged while Hamlet and Fortinbras are made to wait in the wings a bit longer.

When Polonius walks in, Claudius is activated. He rises, enters a secret door, and walks to the chapel, his adviser in tow. This is where Polonius gave his advice to Laertes, a possible source of irony since Claudius is to himself true (unrepentant) which ultimately dooms him. It's also fiercely ironic that a dishonest plan to spy on Hamlet and his mother is laid out on the way to a church. The rapid fire sequence makes it seem like Claudius is getting all his sins out of the way before he goes to confession.
Jacobi's Claudius is clearly haunted by his fratricide, which is what makes him more sympathetic. While he cannot repent, he does feel guilty, and he doesn't ask the angels to forgive him, only for the strength to make amends and do what he must so he can be forgiven. He asks for a conscience. Repentance is a process with many steps, and in Hamlet's world, it seems much easier to go to Hell than it is to Heaven. Something to think about when we get to the ending. Time seems a great enemy in the play. Not only is it fluid and "out of joint", but it's a corrupting influence. The more Hamlet delays, the more death he causes. In Claudius' prayer, he asks to be given the supple knees of a new born babe, an image of innocence that translates not just to the physical. He wishes to return to a time when there was no taint on his soul. Alas, age breeds corruption as sins accumulate. The speech also highlights a certain futility in the plot. Claudius WILL be punished, and the punishment will fit the crime. He knows he's headed for Hell, which is "just" because that is the fate that greeted his victim. So the question is, does Hamlet have to kill him? God will sort it out, and in a sense, that's what Hamlet's delay tells us. Killing Claudius is just another regicide, one that may doom Hamlet's own soul. In Hamlet's highly religious world view, however, Claudius must be killed before he can be forgiven for his sins through confession or final rites. Of course, the fact that Claudius doesn't believe he can be forgiven means only the audience is aware of revenge's innate futility here.
Once Claudius takes on a praying position, Hamlet appears on the priest's side of the confessional, in a position to forgive or to dole out punishment. He dictates morality in the play. He slides his dagger through the window, his words heard in voice-over as to make the scene less theatrical, and the blade goes right into Claudius' ear, shockingly. It's a fantasy. The next shot shows the blade not quite there yet as Hamlet hesitates. We're on Hamlet's eyes, thinking, realizing, and remembering. Quick flashbacks take us to various points in the film where Claudius was a-sinning, which includes a shot of the King and Polonius getting behind an arras. A clue that Hamlet very much knew that they were behind the mirror during "To be or not to be"? Or an imagined moment based on what he later learned? Choosing to wait for a better moment, the blade passes before Hamlet's eyes and he is gone. Claudius' ironic last line is also in voice-over. A strange feeling comes over him and he looks to the priest's side, but there's no one there. I wonder, could there be a staging where Hamlet isn't there at all, but is instead Claudius' imagined Hamlet, first punishing him, then not, then resolving to do so at a different moment, fueling Claudius' paranoia and justifying the exile? Hamlet as guilt manifest.