When I try to update a dataset I get an error that the system is unable to find "Table"?

Are you calling Update on the dataset like this without specifying the name of the table that you are updating. The problem is that when table names are not given the system assumes a table name of 'Table'. This of course causes the update to fail.

this.dataAdapter.Update(this.dataSet);

If so just change this line to

this.dataAdapter.Update(this.dataSet, "Customers");

// replace 'Customers' with the table that you have