In Visio 2010 and 2013 is implemented a new concept: the container.
In cross functional process flow diagrams this is used extensivly.
Because Visio 2003 and 2007 don't know containers, the can't open or work with such diagramms.
The only way in such a mixed environment is to use only Visio 2003/2007 to create and edit such diagramms.
Visio 2010 and 2013 should only be used to open and look at such diagramms.
AFAIK: Because they (2010/13) convert this diagramms to their container-version, when opening, you shouldn't even save such a opened diagramm when closing because it's converted afterward and then unusable for the older versions.