] At first blush, Polonius seems like comic relief but, throughout the play, Polonius hides behind a mask, appearing to be many things. In reality, he lies, manipulates people (including his children) and eavesdrops on others' conversations. Polonius' appearance is not his true nature; behind the mask there lies someone totally different.
....Polonius is really all about appearances, isn't he?
I think P's suggestions to eavesdrop on Hamlet (as well as setting a spy on his own son) is merely establishing once for all that P is not the upstanding citizen he would have us think he is, and perhaps that he's something more than a windbag, as well.
] In many ways, Polonius and Claudius are two sides of the same coin.
] Unspoken is the acknowledgement that Polonius possibly also helped with the murder.
Eh - I don't know that I can take it this far.
Polonius wants to be thought important - indispensible - "what would Claudius do without me?" He spouts "wisdom" to his children, and offers his counsel to Claudius as if his word should be taken as gospel, but I see little real Ambition in him. I think he's happy with the "control" he feels he has over the king already - and I find it difficult to imagine he would have openly conspired to murder King Hamlet. Am reminded (*snort* really! Couldn't help it!) of Harry Potter - POA here - in reference to Wormtail, in thinking that Polonius wouldn't have been willing to swear THAT kind of allegiance to Claudius until he knew C was "the biggest bully on the playground". As long as King Hamlet was alive, he wasn't.