It’s generally accepted* that when you are using an OLE DB Source or an ADO.NET Source, you should specify all the columns, rather than selecting the table from the dropdown, or using a SELECT * SQL statement.
If you’re like me, then you probably don’t have the columns in all your tables memorized, and you don’t like typing, so getting a complete list of columns is a bit painful. You either have to use the query designer to create the whole query, or go to SSMS and create the SELECT statement from there. However, there is a simpler way. Just type “SELECT * FROM [your table here]” into the source component’s SQL Command box, and then click the Build Query button. The query designer will automatically expand the * into the specific column names. Just click OK as soon as the designer opens, and you end up with a fully populated column list.
*For some of the reasons why this is generally accepted from an SSIS perspective, see these posts from Jamie Thomson: http://blogs.conchango.com/jamiethomson/archive/2006/02/21/SSIS_3A00_-SELECT-_2A002E002E002E00_-or-select-from-a-dropdown-in-an-OLE-DB-Source-component_3F00_.aspx and https://blogs.conchango.com/jamiethomson/archive/2006/01/05/2554.aspx (point #4). If you want reasons from a general SQL standpoint, search for “never use ”SELECT *” in SQL” in your favorite search engine.