The Problem with Dawkins' Weasel Metaphor

A variation of the teleogical argument for the existence of God is the monkey's typing on  typewriters.  Evolution comes by pure chance.   Getting life as we see it today is about as likely as a monkey hacking away on a typewriter producing a Shakespearean play.  In other words, not very.
Take the line from Hamlet:

Methinks it is like a weasel

There are 28 characters in this phrase.  Each character can be one of 29 characters (28 letters +blank spaces).  So, the odds of a monkey randomly typing this are 29^29= 1 in 8.85*10^40.  That's just a part of the code.  If Hamlet is 4042 lines like this, then the odds of the monkey getting Hamlet by become much less.  If the monkey types at one stroke per second, it takes the monkey 31 hours to generate a draft.  Unless our monkey is lucky, we are waiting a long time for him to get it right. It's easier to see someone writing the play than a monkey getting lucky just like it's easier to see Someone guiding the development of life, specifically a DNA molecule, than random chance.
Richard Dawkins takes a stab at this argument with his weasel example (it actually involves weasels, I'm not talking trash about Dawkins)
HT to arstechnica:
At the other end of the spectrum, we have the weasel program, first discussed by Richard Dawkins in The Blind Watchmaker. In this example, the target text is the Shakespeare line "Methinks it is like a weasel." The random typing of characters is considered to be analogous to the results of random mutation. But Dawkins adds a new step, analogous to natural selection: if any of the letters are right, they're retained as "fit." The rest get reshuffled and are tested again. Adding this selection step radically shortens the time it takes to arrive at the correct solution, since the monkey will never have to throw out any of its successful work and start over. 

Dawkins treats DNA as a storage unit for evolutionary information.  Organisms that do not have the required DNA are weeded out about via death.  This acts as the fit he refers to.  It eliminates repeat steps and makes the weasel more likely to type up a play though the odds remain 29!=29*28*27...1=8.84*10^30

The problem is that most mutations are either harmful or benign.  Instead of acting as a place holder, they act as erasers in these circumstances.  So, one mutation might help Dawkins' weasel get the M but the next one will probably erase the M (or the e or the k depending on how the far weasel goes) and send him back to the start.  Mutations create a problem for Dawkins, they do not help him and are still highly unlikely to get this by chance.