I have a form where any lookup with a filter on it is not working for certain users (lookup controls and calculated values using lookup functions). The account that created the form and the SharePoint service accounts work fine but not anyone else. The account that created the form was in the owners group and everyone else was in members so I moved the working account to members and it still works. I moved another person from members to owners and they still do not work. Cache was cleared and browser restarted for each test. There are no special permissions throughout the site (except for on the style library and image library), all others are inherited from the site. Lookups without filters (on the same lists) work fine for everyone.
Another thing I noticed which might not be related is if I edit the form as a member (even the person who created the form) then I cannot save changes to any controls (no error it just acts like I'm not clicking save) but I can publish the form. Change it back to an owner and I can save ok.