I've never really liked the construction "There is..." to indicate existence. I love English, but I think of this as one of English's little foibles. Indicating the existence of something by constructing a meaningless subject and relegating the actual subject of your sentence to being the object? Please. Give me a break. :-)
But now, I'm beginning to expect that English is evolving a more elegant solution. "There's" is now being used not as a grammatical subject, but rather as a rough equivalent to the existential quantifier of symbolic logic, ∃, which means "there exists".
Quirk of grammar: this behaves differently from its uncontracted origin 'there is' in that it freely accepts a plural co-subject*. So 'There's three men in the garden' is grammatical, whereas it's not with 'There is'.
* I'm at work so can't check what the proper name for this item is: the 'three men' in my example. The subject is the noun 'there' (sic - it's a noun, a pronoun to be precise). The other is co-subject, associated subject, extrapolated subject?