是 does not connect two nouns in "有什么事是我该做的吗?"
In short, the second noun "事" is omitted.
The complete sentence should be like this: 

有什么事是我该做的(事)吗？




For more, in Chinese, the attributive clause goes before.

The proper way to translate "Is there anything I should do?" is "有什么我该做的事吗？