Unfortunately, I don't remember where I read this, but the most interesting Shakespeare audition that I've ever heard of was also the simplest: The director would assign each actor to read one of the sonnets. That was it. Because all of the skills required to interpret a part are exactly those needed to properly read a sonnet. In fact, reading poetry (despite its incorrect reputation) is actually a highly creative activity. It requires intellect, emotion and practice - the more we do it, the easier it gets. Also, the plays themselves (as I've said before) are best understood as large-scale poems - so assigning the interpretation of a small-scale one is probably the best way to measure a Shakespearean actor's skills. Ready to try one? Here's Sonnet 17:

Who will believe my verse in time to come,

If it were fill'd with your most high deserts?

Though yet, heaven knows, it is but as a tomb

Which hides your life and shows not half your parts.

If I could write the beauty of your eyes

And in fresh numbers number all your graces,

The age to come would say 'This poet lies:

Such heavenly touches ne'er touch'd earthly faces.'

So should my papers yellow'd with their age

Be scorn'd like old men of less truth than tongue,

And your true rights be term'd a poet's rage

And stretched metre of an antique song:

But were some child of yours alive that time,

You should live twice; in it and in my rhyme.