'Store' in this context sounds very much like a Repository or Service. In that case, this is an extremely common pattern. The flaws/problems will vary with your implementation and the problem domain.
On a general level, it sounds like the book is using 'Store' to represent a level of business logic + a level of data retrieval logic that handles a set of data that may or may not be part of your application.
For instance, wrapping the twitter api in a 'Store' is a nice way to compartmentalize that logic.