A common fair use issue arises with photocopying copyright protected materials. For example, if you wanted to photocopy a copyright protected magazine article to distribute to students, there could be a finding of fair use under certain circumstances.
For more information about the minimum amount of copying allowable for classroom use, see http://www.copyright.gov/circs/circ21.pdf.
Another common fair use issue arises with posting materials on Blackboard. Generally, streaming a short film or music clip from an authorized copy will be allowed. However, it is absolutely imperative that you examine the four fair use factors listed above.
For more information on fair use and media items, see the Music Library Association's Fair Use Guidelines at: http://www.lib.jmu.edu/org/mla/Guidelines/Accepted%20Guidelines/Copyright%20and%20Fair%20Use.aspx