We would like to upgrade our software from Access 2003 to Access 2007.
Why would you do that? A2007 is 16 years old and out of support. Why not upgrade to the newest version? The only reason to not skip A2007 is if you have .mdb's that were actually created with earlier versions of Access. In that case, convert them to A2003 first, and then upgrade to the newest version.
As
@sonic8 said, the conversion should be straight forward. I've never had any issues converting applications to the ACE version of Access except for the issue with the calendar control. A2007 and newer have a built in calendar control. If the field is defined as a date or if the unbound control is formatted as a date, then the internal calendar is automatically available so removing the old ActiveX calendar is trivial. You just may have to do it a lot. Referencing this old ActiveX control which is no longer supported will cause compile errors. So, make sure all modules have "option Explicit" specified and all modules must compile cleanly. This is best practice anyway so hopefully, this doesn't cause you a lot of work. If you use other ActiveX controls, you will also need to find replacements for them or give up the functionality.
Another thing you might need to do is to disambiguate DAO or ADO objects, whichever you used. That means that you need to find all the Dim statements for DAO/ADO objects and change them to
Dim db as DAO.Database, etc
One final thing, as long as your .mdb's are at least A2003, you can run them in the newest versions of Access without actually converting the apps. I would still do the conversion but, you can do it at your leisure.