In Hamlet, what does the scene with Polonius and Reynaldo suggest about Polonius?
The little scene between Polonius and Reynaldo at the beginning of Act II characterizes Polonius as an old windbag who is suspicious of everybody, but it is primarily intended merely to establish that Laertes is now in Paris. That was a considerable distance from Denmark in those days. Laertes actually had to travel there by ship. Laertes has a very important part to play in the final acts, but Shakespeare wanted to keep him out of the way until he was needed. If Laertes had been present at Elsinore when Hamlet killed Polonius, the whole story would have been different. But it will take a long time for Laertes to receive the news of his father's death, and then it will take a long time for him to get back to Denmark. In the meantime he would only be in the way. Shakespeare introduces him very early in the play but then immediately sends him off to France. He wants the audience to recognize him when he returns in a fury, but he has no need for him before that point. His impetuous arrival adds spice to the finale. Then it will be Laertes who kills Hamlet.
This scene shows a couple of things about Polonius' nature and his view of people. The fact that he deems it necessary to send someone out to spy on his son suggests that he does not think people are trustworthy, even his own offspring. He asks Reynaldo to "fish" for evidence of his son's wrong doings, and hopes that by trickery he will find truth.This shows that he thinks that by being underhanded he can get more than by being straightforward. He fancies himself wise, but as we know, he is less wise than he thinks he is.
The strategy he employs with his son reveals a weakness in his character:the inability to deal directly with people. This need for subterfuge ends up costing him everything, including his own life and, though he is not around to witness it, the life of his daughter.
Polonius' instruction to Reynaldo are so "tedious" that this scene is often cut from modern productions of the play. It reminds the audience of his earlier advice to Laertes and Ophelia and foreshadows his overlong talk with Claudius and Gertrude in the next scene. All the conversations show that Claudius is subject to long-winded explanations and advice that sometimes appears to have no point. Even Gertrude recognizes this when she pleads with Polonius in Act II, Scene 2, to shorten his explanation and tell it with “More matter, with less art”. Polonius himself recognizes that he can't remember what he was saying when he tells Reynaldo, “What was I about to say? By the mass, I was about to say something! Where did I leave?” (Act 1, Scene 1ines 50-51).