Though yet of Hamlet our dear brother's death
The memory be green, and that it us befitted
To bear our hearts in grief and our whole kingdom
To be contracted in one brow of woe,
Yet so far hath discretion fought with nature
That we with wisest sorrow think on him,
Together with remembrance of ourselves.
Therefore our sometime sister, now our queen,
The imperial jointress to this warlike state,
Have we, as 'twere with a defeated joy,
With an auspicious and a dropping eye,
With mirth in funeral and with dirge in marriage,
In equal scale weighing delight and dole,
Taken to wife: nor have we herein barred
Your better wisdoms, which have freely gone
With this affair along. For all, our thanks.
Now follows, that you know, young Fortinbras,
Holding a weak supposal of our worth,
Or thinking by our late dear brother's death
Our state to be disjoint and out of frame,
Colleagued with the dream of his advantage,
He hath not fail'd to pester us with message,
Importing the surrender of those lands
Lost by his father, with all bonds of law,
To our most valiant brother. So much for him.
Claudius is extremely good at public speaking. This is only the beginning of the extended speech that begins this scene, but immediately he is working the crowd. He mentions his dear brother several times - in increasingly loving terms. Our dear brother, our late dear brother, our most valiant brother... certainly nobody could accuse him of forgetting said brother in his new project of running the country. Any comments on the perhaps unseemly haste with which he has married his dear brother's wife are covered by his acknowledgement of this haste, and the sequence of happy/sad images he uses to do so. What's impressive here is how careful and slick his speech is. He leaves no room for doubt - he's the King, and that's that.
As mentioned within the episode, it can be an amusing or a frustrating project to mine any edition of a Shakespeare play for stage directions. Sometimes editors have characters exit at particular points, depriving them of the chance to hear a necessary piece of information. Sometimes entries are likewise re-arranged. As a rule of thumb, I'd personally tend to double check the folio and track through the scene to ensure that no opportunities are missed. A perfect example of this is in King Lear. The play starts with Edmund being introduced - and thereafter he watches the entire scene and all the chaos that ensues. He stays on stage throughout, watches everything, and then is left there when the scene ends. Act I Scene ii begins with his soliloquy, laying out his evil plans. But we need him to have stayed and seen everything first!
Officially Claudius is never named within the play. All of the surviving texts do give him the name Claudius, of course, but only in the stage direction that begins this scene (hence this episode's name!) As with Lady Macbeth, who is likewise never named in her play, the character's status and position are made perfectly clear within the scenes and interactions of the play. We will continue to discuss Claudius' name in coming episodes.