In normal conversation, I use "there's..." for both singular and plural, but more formally, I say "there are.." for plural. Do other varieties allow "there's..." for plural in casual speech?
There is...
The use of "there's" for the plural while using "there are" (and not "there is") for the plural in more formal speech seems to be very common in North American English. I myself use it, even though I also use "there're" as well in even informal speech, and I would guess that most NAE-speakers today use it as well to some extent.
In informal usage, I can have both "there's" and "there are" for plurals, like Travis. For me, this is similar to the distinction between present subjunctive "may" and past subjunctive "might" - I often ignore the distinction, but sometimes I do make it, even in informal speech.
"there are" is correct. "there's" is ungrammatical as it's singular, with the plural equivelent being "there're" not "there's".
I think this began in the US, but it is definitely spreading to England, probably under the influence of US TV programmes.