In the Elizabethan era, the royal crown was viewed as divinely touched and hence any action against the crown was an action against God. Claudius dismisses God's right to control the crown by committing a "murder most foul" (I.v.27), yet he concedes that "there's such divinity doth hedge a king" (IV.v.121). Claudius admits that God influences the monarchy and yet he chooses to violate the divine monarchial progression. Hamlet recognizes Claudius' evil nature beyond simply the murder of his father; Hamlet sees that Claudius is corrupting all of Denmark. Claudius' reign is compared to "an unweeded garden/That grows to seed. Things rank and gross in nature/Possess it merely" (I.ii.135-7), his influence causing the destruction of a previously beautiful environment. Claudius' infectious evil must be eliminated, and Hamlet feels he is the only man who can do anything; he pulls out all the stops and in the end accomplishes his goal.
King Hamlet's "foul and most unnatural murder" (I.v.25) tops Claudius' list of egregious sins, but most of his offenses are psychological rather than physical. Using his mastery of manipulation, Claudius, the "incestuous" and "adulterate beast" managed to win "to his shameful lust the will" of the virtuous queen, Gertrude (I.v.42-6). Gertrude could not be persuaded to switch husbands without a little verbal trickery on Claudius' part, and that turns out to be his true skill: lying convincingly. Claudius manages to legitimize his ascent to the throne by diverting popular attention, away from the circumstances of his ascent, and to the impending attack by the young Fortinbras (I.ii.1-20). Claudius' propensity towards fabrications is in direct violation with the Holy Commandment Thou shalt not bear false witness; hence, he violates one of the pillars of Christian moral law.
Claudius' lies are effective enough to persistently deceive to play's antagonist, Hamlet. Despite Hamlet's disgust with Claudius for marrying Gertrude, and his view of Claudius as "a king of shreds and patches" (III.iv.104), Hamlet suspicion of Claudius as a murderer is preliminarily nonexistent. The appearance of a spirit claiming to be Hamlet's dead father first alerts Hamlet to the actions of "that incestuous, that adulterate beast, /With witchcraft of his with, with traitorous gifts" (I.v.42-3). And yet still, Hamlet remains hesitant to believe that Claudius was the murderer, searching for complementary evidence. The play that Hamlet enacts -- designed to "catch the conscience of the king" (II.ii.562) --succeeds in revealing Claudius' guilt, but does not provoke instant action on Hamlet's part. So effective is Claudius' manipulation of the royal circle that he manages to almost permanently stay the revelation of his guilt, and if it weren't for supernatural intervention against an injustice, he may never have been exposed.
The most odious of Claudius' crimes is his lack of emotion over his traitorous fratricide. Claudius doesn't even give his deceased brother a word of...