Reading points: some matters to consider as you read:

The play's dual focus on public conflict (matters of state, civil war, etc.) and private or personal conflict (within and between various characters and pairs of characters).

Prince Hal and Hotspur as foils: how are the differences in their temperaments, histories, and priorities significant?

Father-son relationships, particularly Shakespeare's great accuracy in portraying fathers and sons in conflict.

The relationship between Prince Hal and Falstaff: what does each "get" from their friendship, and why might such an unlikely pair of friends enjoy each other's company as thoroughly as they obviously do?

Falstaff is generally considered Shakespeare's greatest comic creation: what makes Falstaff such a brilliantly wonderful and memorable character?
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The play's commentary throughout on honor: differing definitions, views, and uses of honor.

 The function of humor in a thoroughly "serious" play. How does the humor in this play compare with the different sorts of humor we've encountered in the comedies we've read? How is the humor an integrally crucial facet of this play?  Beyond simple comic relief, what would the play lose if Shakespeare had not included the comedic scenes?

 The play's commentary on leadership: what makes some characters strong and effective leaders and others less than fully effective leaders?

The burdens of leadership: the tension between personal desires and public responsibilities for those in leadership positions.

Shakespeare's portrayal of Machiavellian politicians, rulers who manipulate others, craftily, for the ostensible good of the "cause" or the good of the state.

The development of Falstaff over the course of the play: while his essential character may not change substantially over the course of the play, consider whether your view of Falstaff does change between the earlier and later scenes in the play.

 The play's continuing relevance: significant applicability in a number of respects to modern readers.