Hamlet's eavesdropping
This film has Hamlet eavesdropping when Polonius directs his daughter
"I would not, in plain terms, from this time forth
Have you slander any moment leisure
As to give words or talk with the Lord Hamlet"
and Ophelia by his command "did repel his letters and denied his access"
Hamlet, rather than suffering "the pangs of despised love," as in the play, now knows that Ophelia is simply following her fathers command, and perhaps has feelings for him. This makes Hamlet cruel and uncaring in the "Get thee to a nunnery" scene.
In the play, Hamlet knows from Rosencrantz, Guildenstern, and Polonius that the King is interested in finding out exactly what he is up to, and that Ophelia has rejected him abruptly two months before. To him she is attempting to effect a reconciliation, but simply because he doesn't know any reason for her change of heart, ("well well well") Hamlet knows all is not what it seems, and she does not explain, rather takes the approach that the break came from him. He presses her and she cannot give him a straight answer. His lunacy is designed offensively to flush out the King and make him play his hand, and as a defense, to mask his true feelings. Ophelia represents a considerable threat, being able to penetrate his defenses, and his brutality towards her is an attempt to warn her off. While he would still love her, he would not imagine he could hurt her personal feelings, as she would not be genuine.
However in the film, because of the eavesdropping, Hamlet knows she still has feelings, that her father has only forbidden her, so his actions are much crueler. It comes across as not forgiving her weakness for not refusing her fathers command.
Also the bit where he "raises a sigh so piteous and profound" in visiting Ophelia makes no sense if he knows Ophelia is obeying her father, unless Hamlet is using Ophelia to trigger the whole "bait-with-Ophelia" setup, which is too machiavellian.
Overall this makes Hamlet's protestations of love at Ophelia's funeral hollow, his motives less interesting, and his death less tragic. That Mel pulls it off is to his credit. He artfully conceals it as schizophrenia, along with the mother love, as the madness allows him to.
Also the "Nymph. In thy orisons be all my sins remembered." line, as used in this film as a greeting to Ophelia, makes no sense. I cannot imagine a gentle wooer calling the woo-ee a nymph, from which nymphomaniac is derived, in the 16 century, though it is of course a great compliment in the 21st. For mine Hamlet says this to himself sarcastically, urging her inwardly to dwell on the imagined shortcomings that have led her to reject him, and calling her an erudite slut under his breath as a disappointed male lover might. In this film, it is presented as Hamlet urging Ophelia to pray for him! Luckily Hamlet is mad. However calling Ophelia a nymph seems inappropriate at the start of the "words of so sweet breath" scene. It would put Ophelia off. After it, perhaps yes.
If Hamlet does know of Polonius' influence, it would make the "fishmonger" scene more understandable, giving Hamlet a strong motive to bait Polonius. But if he does not know Polonius exact role, he could still call him a fishmonger, slang for pimp, if he can call his daughter a nymph.
So this eavesdropping does not work for me!