I think the most common way a native English speaker would say that sentence is, "There's 10 dollars in my pocket". The contraction of "There" & "is" is much more natural than saying "There are...". Perhaps that is why they wrote "There is..." instead of "There are".

You are right to be suspicious here - I'd say it's wrong. It should be "There are 10 dollars in my pocket". However, "There is a 10-dollar bill in my pocket" (where the bill is the subject instead of the dollars) would be fine.