The First and Second Tooth

John Dover Wilson pays a considerable amount of attention to what he refers to as "the problem of the dumb-show." He assumes that the dumb show with which The Murder of Gonzago begins is intended either as a tableau to foreshadow the contents of the play to follow, or as a way of representing scenes necessary to the plot which will not be put into dialogue. What troubles him is why Claudius sits through the action of the play in compressed pantomime and does not react until the poisoning scene comes around a second time -- this time with dialogue. Wilson takes exception to what was called the "second tooth" theory -- the idea that Hamlet is deliberately testing Claudius twice, and that Claudius' nerves stand up to the first test, but fail at the second.  

Prior to the 20th century, productions often demonstrated sufficient patience with the scene to enjoy the double test.

Hamlet would have thus a double opportunity of catching the conscience of the King.
 - Edward Dowden (ed.), The Works of Shakespeare, Bobbs-Merrill, Indianapolis. p.116.

Wilson, however, finds the need to conduct the text twice to be dramatically inefficient.  In this regard, he reflects a modern sensibility.

Mr. Granville-Barker, who accepts this interpretation, tells me that it is quite actable on the stage... Yet, if a layman may be so daring, I cannot help thinking that the double text is less dramatically effective than the single one.
   - John Dover Wilson, What Happens in Hamlet, Cambridge Univ. Press, London, 1935. p. 151.

Here's how Harley Granville-Barker, the director, describes his staging of the scene.

When the King sees the Dumb Show he is at once alert. Though here may be a coincidence and no more, whatever Hamlet has a hand in will now be matter for suspicion. But what should he do? If the thing is mere coincidence, nothing. If it is a trap laid, he is not the man to walk straight into it -- as he would by stopping the play for no reason he could give before it had well begun. He must wait and be wary...

"Miching mallecho...mischief...tell all."; Claudius must be wary indeed.
Here, then, is the battle joined at once, between the watcher and the watched. On the defensive is the King, whose best tactics, without doubt, are to brave the business out, calmly, smilingly, giving no slightest sign that he sees anything extraordinary in it.
 - Harley Granville-Barker, Prefaces to Shakespeare, Princeton Univ. Press. Princeton,1946. v.i. pp. 87-88.

We know that Hamlet expect the scene to have its effect with one speech.  There is no mention of the inclusion of a mime that could steal that speech's thunder.

Observe my uncle - if his occulted guilt
Do not itself unkennel in one speech,
It is a damnéd ghost that we have seen, (III,ii,75-77)

Wilson makes a point of the fact that both before and after the play-within-the-play, Hamlet talks of the "one speech" or of the "talk of the poisoning" as the thing that activates Claudius' reaction, not the action of poisoning itself. He says that it is the language of Lucianus' speech (played by the First Player) that triggers the mouse trap. Wilson further concludes that it is the language from the "dozen or sixteen" lines that Hamlet wrote for inclusion that pricks the King into rising. He even says that Hamlet had not anticipated the dumb-show, and worries that it will take the edge off of his speech. What saves the effect of the speech is that the King fails to pay attention to the dumb-show.

Productions inspired by Wilson's interpretation have the King entirely ignoring the pantomime.

The King was not looking at the dumb-show; he was doing something else. What was he doing? Halliwell-Phillipps long ago suggested that he missed seeing the show because he was talking to the Queen while it was going on. This is in part the true explanation. - Wilson. p. 159.

The dumb-show enters, performs its brief pantomime -- a matter of a few moments only -- and passes out entirely unnoticed by the disputants; and when the audience turn again to see how this silent representation of his crime has affected the King, they find him still closely engaged with Gertrude and Polonius. - Wilson. p. 184.

None of these stagings of the play scene address the question John Dover Wilson raised about the dramatic efficiency of including a piece of actions which is meant to be ignored or blurs the dramatic focus of the scene. Ultimately, the question becomes one of whether the mousetrap is is baited with the event depicted on stage, itself, or the language that accompanies that event. For Wilson, the answer is found in the text, not in the staging.