No, I don't mean that he'll be to popular music in this decade what Dylan was to music in the 60s. No one could; the cultural economy of "popular music" has changed in ways that fairly effectively bar a repeat performance.
Nor do I think that Eminem is Dylan's musical heir. Trying to trace a line of influences from the one to the other is an exercise in radical attenuation.
Instead, I'd like to suggest that Eminem has latched on to Dylan's personality: he may well be the best modern exemplar of the Trickster figure that Dylan embodied back when, well, back when he was still Dylan.
Eminem is -- as was Dylan in his day -- a lyrical prodigy who is nonetheless jaw-droppingly inarticulate when not actually performing. He has Dylan's dismissive sneer, Dylan's corrosive cynicism, Dylan's casual, pervasive misogyny. Dylan has always had a talent for mockery, for turning the character flaws of others into art ("Like a Rolling Stone," anyone?); this talent has sometimes seemed inseparable from his ability to befoul the lives of those who make the mistake of loving him.
Would the original Slim Shady please stand up?