What are Hamlet's weaknesses and strengths from act 1 to act 4?

Hamlet in Act 1 is overcome by grief at this father's loss, and enraged by his mother's inappropriate, in his view, marriage to King Hamlet's brother.  One of his major shortcomings, through out all of the text, until the end at least, is his lack of concern for the welfare of the state.  He is concerned that an unjust king, Claudius, is on the throne, but he is more concerned with revenge than the leadership of the country.  He is, after all, next in line to the throne!  It is not until after he sees Fortinbras willingness to sacrifice thousands of lives for a useless piece of land that he is finally able to put his personal intellectual musings aside (Look at each of the soliloquies in Acts 1-4: dad is dead and mom's tainted, should I live or die, etc. until act 4:  "My thoughts be bloody or nothing worth!")  His weakness and his strength are intertwined -- to act hastily and kill a rightful king would put the country in jeopardy from its enemies, not to mention end his own life.  However, his hesitations and need for intellectual proof, coupled with his impetuous action in killing Polonius, bring about the rest of the deaths in the play.