What can I use in place of shiitake mushrooms?
While shiitake mushrooms do have a distinct and identifiable flavor, the reason dried skiitake mushrooms are added in broth and stock making is for the umami.  The flavor of umami is the result of the glutimates available in dried mushrooms (as well as other ingredients).  While shiitake mushrooms contain a lot of glutimates, any other dried (or even fresh, though you will need more) mushrooms are a suitable substitute.  Barring that, you could use other ingredients high in glutimates, such as tomato, or the rind of an aged cheese, like parmesan.  Alternately you can add a sprinkle of MSG, as that is simply the sodium salt of the glutamic acid that is naturally occurring in the ingredients mentioned.  Don't go too heavy on the MSG, though, as your broth will take on the flavor of dashi...unless, of course, you are making dashi.