Like many members of the royal family throughout the years, Claudius is a multi-faceted human being. On the one hand, he is cold, cruel, calculating, and ambitious. He has proven he will do anything to get the throne (including murderering his own brother and marrying his wife) and anything to keep it (he has launched several plans to murder young Hamlet and he succeeds!) One thing that is unforgivable in him is that he brings others into his evil machinations, sullying their reputations in the process. Evil people are never happy just being evil...they are happiest when they drag others down into the mud along with them to suffer in company.
On the other hand, he seems to be a good leader and politician. Gertrude and other officials accept him as rightful husband and leader of the land. He makes decent decisions where Fortinbras is concerned and has good relations with England, as illustrated by the quick carrying out of Claudius' request to dispose of Rosencrantz and Guildenstern.
He is also quite loving to Gertrude which is commendable, all things considered.
Regardless of his good points, like Macbeth, Claudius goes down as a villain in the books since he does not live long enough to illiminate the good qualities he possesses.
Claudius is corrupt in that he committed murder to gain the throne and to get Gertrude. He is also corrupt in that he is planning to have Hamlet killed, first by the British and then when that doesn't work out, he and Laertes plot to cheat in a fencing match and kill Hamlet that way.
Claudius does seem to be pretty good at politics. He knows sends ambassadors to Norway to fend off Fortinbras' attack and he seems to know the mood of the people of Denmark pretty well. That is evidenced when he says he knows the people love Hamlet and later when he fears the people will blame him for Hamlet's killing of Polonius.