The characteristics that Polonius displays in act 2 are pretty much the same as in the rest of the play. For one thing, he's incredibly devious and manipulative, sending Reynaldo to spy on his son, Laertes, in Paris. Polonius encourages his loyal servant to make up stories about Laertes's wild ways that he can tell to other Danes in order to find out what he's really been up to. Reynaldo is to pretend that he vaguely knows of Laertes and his supposed reputation for loose living. Then when he casually mentions it to Danes he meets in Paris, they can either confirm or deny what he's been getting up to:
“And in part him, but,” you may say, “not well. But, if ’t be he I mean, he’s very wild. Addicted so and so.—” And there put on him What forgeries you please. (act 2, scene 1)
Polonius gives Reynaldo carte blanche to make up all kinds of lurid tales about Laertes. This is simply to get a reaction from Danish expats, which will then confirm to Polonius just how his son's been conducting himself.
There's more than a hint of smugness about Polonius. He seems perpetually dazzled by his own wit, erudition, and seemingly endless capacity for devising ingenious schemes. And so it proves here:
(And I believe it is a fetch of wit)
This is Polonius openly bragging about how great he thinks his plan to check up on Laertes really is. Humility is not one of his strong points; we might say that he's too clever by half. Unfortunately for Polonius, his penchant for crafty scheming will ultimately prove his undoing.
As well as being devious, Polonius also shows himself to be a grossly uncaring father, contemptuous of Ophelia's privacy and insensitive towards her emotional needs. He and Claudius cynically use Ophelia as a guinea pig in a psychological experiment to determine the nature of Hamlet's madness, if indeed madness it is. As Polonius and Claudius hide behind a curtain, Hamlet subjects Ophelia to a vicious tongue-lashing which reduces her to a crying mess. Yet, Polonius offers his poor daughter not a single crumb of comfort. As far as he's concerned, the most important thing is to find out what's been eating Hamlet lately; his daughter's feelings don't enter into it.