Polonius may be seen to lose his grip in his bouts of prating to the King and Queen in parts of the play too. His speech to Claudius and Gertrude concerning Hamlet's madness is a prime example of Polonius' prattling, as we see in his long-winded build up to his conclusion, that Hamlet is mad;
Therefore, since brevity is the soul of wit,
And tediousness the limbs and outward flourishes,
I will be brief. Your noble son is mad.".
His prating in this scene can, in some, undoubtedly raise a cynical smile; Polonius is interpreted as a comical character; the fact the Queen demands "More matter with less art." is coupled with Polonius' artful way of denying he'll use it is a prime example of the irony in this scene. He can be therefore viewed as a clownish figure by many audiences.
It may be the case, despite the irony displayed in his choice of words, that he is simply afraid of being the purveyor of bad news, especially news he delivers after being wrong about Hamlet's madness. But, as we see, after Polonius asks the question "What do you think of me?", Claudius answers "Of a man faithful and honourable.". If Claudius was to think otherwise, it would be obvious Polonius would not be Secretary of State.
Polonius' pomposity can be seen in Shakespeare's presentation of him in his scene with Reynaldo. He relates to Reynaldo on a high, somewhat elitist level, referring to himself "of wisdom and of reach". He may be presented as pompous in the scene with the King and Queen concerning Hamlet's madness also; from the prating displayed in an earlier quote he may be interpreted by audience as someone who is showing off his intellect, language skills and deep thought.
Despite this, Polonius has not been wrong in the past; he may have "the right" to be as pompous as he is, because his actions have always been right before, and he thinks they will be now.
It is also arguable that Shakespeare presents Polonius in his dealings with his son Laertes as authoritative and over intrusive, and somewhat of self-interest. In the key scene with Reynaldo, one can assume that Polonius' list of activities that he wishes Laertes to be restrained from, including "drinking, fencing, swearing, quarrelling, / Drabbing...", that Polonius wants no "scandal on him". His methods of finding out the truth, especially the apparent loss of grip on his speech (possibly being a trick) suggest that Polonius is not concerned about Laertes' well-being; rather he could be worried his family's reputation.
However, Polonius can be seen as very sensible in his advice to Reynaldo in relation to Laertes; although it is restrictive, he does say to allow Laertes to have fun; also, in his advice to Laertes, concerning things such as friends: "grapple them unto thy soul with hoops of steel"; clothes: "costly thy habit as thy purse can buy"; money: "neither a borrower or a lender be" and socialising: "Give each man thy ear, but few thy voice" he is very succint and wise in approach. The last two lines, "Thou canst not then be false to any man. Farewell, my blessing season this in thee.", can be seen as very selfless and purely for the good of his son. Furthermore, Laertes' apparent and civilised respect found just as Polonius enters later, remarking that "A double blessing is a double grace; Occasion smiles upon a second leave." again shows Laertes' courtesy towards his father as a very wise man and a person of great importance to him.
Later in the play, seemingly in another act of parental restriction, Polonius is presented to involve himself in relations with Ophelia and Hamlet in a meddlesome manner. He does not want a daughter that would succumb to what he thinks Hamlet is after: sexual relations, and those alone. Shakespeare could be presenting Polonius as using a lie as an example to sway her, and he says how he does "know, / When the blood burns, how prodigal the soul / Lends the tongue vows.", maybe having her taking his view and keeping away from Hamlet, even though Hamlet seems to need Ophelia as someone to trust and rely on in a harsh time for him.
Despite the fact Polonius can be seen to be "over-intrusive" with Ophelia, lying to her to sway her opinion of Hamlet, this may be in order to keep her safe. If he really has experience in matters of love, and that he does "know, When the blood burns, how prodigal the soul Lends the tongue vows.", this experience lends credit to Polonius' dismissal of the authenticity of Hamlet's intentions, especially with reference to Hamlet's "larger tether" and how he can get away with more. It also adds credibility to his opinion of Ophelia as susceptible to fraudulent affections; and it seems very good parental control and advice (even though it does not work out), especially when we find that Ophelia remains attentive, and that she "shall obey, my lord.", echoing Laertes' appreciation of Polonius' authority.
Polonius may also be seen as a conformist, and someone that will happily change his views of a person to make them happy and improve his image upon them. This idea is presented by Shakespeare in the discussion of cloud shapes Polonius has with Hamlet, where Hamlet tests Polonius to see if he conforms to his "thoughts". As a result, Polonius falls into the trap and agrees with Hamlet on three very different shapes; "Do you see yonder cloud that's almost in shape of a camel?" "By th' mass and 'tis, like a camel indeed." then a weasel, and finally a whale. However, Polonius is probably frightened of Hamlet by this stage, and is could be interpreted as not wanting to annoy him, in fear of his own safety.
As we tend to sympathise with Hamlet, we also agree with him on certain matters. However, he does remark to the players to "look you mock him not", suggesting a recognition of the respect Polonius still deserves from others not involved in his 'battle', and as a result we see Polonius, presented through Hamlet's eyes as an important person. Polonius is also seen in a better light after Hamlet has killed him, where he makes cruel jokes about his corpse; when asked where Polonius is, Hamlet speaks of him being at supper, “Not where he eats, but where he is eaten; a certain convocation of politic worms are e’en at him.". From this, we view Hamlet and his actions in a more inhumane way, especially as Claudius acts in a much more favourable manner in response, pronouncing "Alas, alas!" after he realises what has become of Polonius. It is evident through the shock of the King, Queen and Ophelia's response to Hamlet's less agreeable actions that Polonius is a very important man to Claudius, Ophelia and Gertrude.
The aftermath of Polonius' secret burial has large effects on many; his people go into uproar and when news travels to Laertes, he, in a fit of rage, declares he will go as far as eternal damnation to seek revenge. The people of Denmark are “muddled, thick and unwholesome in their thought and whispers for good Polonius’ death” and rise in rebellion to make his son king. It is safe to say that if Hamlet was truly right about Polonius' knavish qualities that there would be no after effects of his death.
After, when Laertes' followers leave, Claudius manages to calm Laertes a little. However, when Ophelia enters and starts singing of a funeral, where “in his grave rained many a tear”, Laertes is distressed and angry at the person she has become since her father’s death. He is presented by Shakespeare as the man Ophelia loved, characterized by her mixing of love and death songs. Act 4 sees Ophelia drowning due to her madness, reported by the Queen to Laertes;
"One woe doth tread upon another's heel,
So fast they follow: your sister's drowned,
Laertes"
The influence Polonius' death had on Laertes to revenge his death is seemingly all that is on his mind now he has lost all his family.
Polonius is undoubtedly a victim of an untimely death; he would have never have known Claudius was a cold-blooded killer, nor that Hamlet could have been capable of killing until he realised Gertrude was in danger when behind the arras, his place of death. Hamlet sees Polonius as an important factor in two issues: the first being his involvement with the quick change of throne after his father's death, where Hamlet suspects Polonius as the reason he lost out on reign over Denmark, as it is probable that Polonius helped Claudius into power while he was away; and secondly, the guessed interference with Hamlet's relations with Ophelia, and how they degenerated quickly over time.
Polonius, although relatively foolish in certain actions, is an innocent man. He arguably does everything for his children in their best interests, and is loyal to the King and Queen. It is fair to say he is a victim of his own eavesdropping, although he does it to prove what he believes is the truth, and therefore what is a threat to who and what are important to him.
I would conclude that Polonius is very much the amiable and sensible father many theatre productions make him out to be. Not only is he amiable and sensible, but his impact within the play is quite enormous. His speeches represent the themes of the play: corruption, and the difference between appearance and reality. Even after his untimely death, Polonius seems to reach into every aspect of Hamlet. He encompasses so many elements of the play; perhaps more than even Hamlet does; and is arguably the most important character in the play.