Can an American citizen, living in the US near the Canada/US border, work in Canada legally? What paperwork/permissions are required? (There is a position in the film industry I am interested in and would like to apply, but am not willing to jerk around the employer if this is not possible.)
US citizens do need a work permit or visa to work or run a business in Canada.
Your chances of getting the job depend a lot on the job and your uniqueness.
A well known actor will have no difficulty. A set designer with a recognised personal style should be ok. A 5 year experienced rigger might have problems because Canada can likely fill that job with local labor.
For American work in Canada, you should get TN visa.
Under NAFTA, the TN Visa or TN-1 Visa enables Americans to work in Canada.
From Wiki: TN Status:
TN status or TN visa is a special non-immigrant status in the United States, Canada, and Mexico that offers expedited work authorization to a citizen of these countries.