I think (but I’m not a native speaker) that formally, the verb should go with the grammatical subject, so it should be ‘there are a book and some pencils on the desk’.
But, in real life, colloquial use, apparently many native speakers feel ok about ‘there is a book and some pencils on the desk’ while they do not feel ok about ‘there is some pencils and a book on the desk’ (because the first noun to follow the verb is plural). Perhaps also the ‘distance’ to the verb matters: many people don’t have any trouble with ‘when you turn here, there is a grocery shop on your left and a bakery on your right’, or ‘there is a book in my bag and some pencils on the desk’.
Also, I think the meaning of ‘there’ in the Jim and Jack sentence is different from the meaning of ‘there in the books on the desk sentence.
I like this website: http://owl.english.purdue.edu/owl/