] I had trouble reconciling this noble trait with his rash, callous killing of Polonious. He didn't hesitate, or even think, but just attacked him without even knowing who it was behind the curtain - and doesn't really show any remorse afterward.

Well, of course, he believes he is killing Claudius, not Polonius. Think about what has just preceeded it. The play. Proof to Hamlet that Claudius did kill his father. He is fired up. "Now I could drink hot blood." He had an opportunity to kill Claudius when he was praying, but didn't do so - "This is hire and salary, not revenge!" Ah, but hiding behind an arras, eavesdropping, sneaking around and spying as Claudius has always done, when Hamlet's emotions are on the edge and in the midst of a confrontation with his mother - that is a good time to do the deed!

] How could Hamlet ponder on and on about the nature of life regarding killing Claudius, but just shrug at Polonious?