It is considered informal by some:
Other grammar books state that the above rules are only for informal English. They say that in formal English, you should always use a plural verb with a series of nouns, even if the first noun is singular. Consider Azar’s Understanding and Using English Grammar, which states: “Sometimes in informal English, a singular verb is used after there when the first of two subjects connected by and is singular. For example:
Formal: There are a book and a pen on the desk.
Informal: There is a book and a pen on the desk.”
Check out the ensuing discussion, too. Quite curious.
There are a book and a pen on the desk sounds quite odd to me. But then again, who am I to judge. Anyway, I found this explanation as to why a singular verb is more natural quite interesting:
"... pressure toward agreement between an inflected verb and the linearly closest NP is attested in the human language-processing mechanism.
Of course, speakers would generally not judge sentences like A dog and a cat is in the yard as
acceptable, so why should they judge There’s a dog and a cat in the yard as natural? ... I suggest that this
is due to a combination of the general tendency toward local agreement plus the temporary
ambiguity induced by having the verb precede the relevant NP. ... in (16a) there is a point at which all one has heard/read is There is/are a book... This temporary ambiguity makes plural agreement with a singular
first conjunct sound initially bad, and singular agreement sound correct; apparently, our judgment
system never fully recovers from this preliminary impression." [Emphasis mine]
(*16a There’s/is/are a book and a pen on the desk.)
I personally suggest just sticking with there's at all times. Problem solved. :-)