Ron Murray, a colleague at the Library of Congress (and no known relation to me), sent me a note about the history of the term "mash-up" in the Oxford English Dictionary (subscription required). The definition of the first sense is "A mixture or fusion of disparate elements" with the notation that usage is rare before the late 20th century, and the OED includes this quotation:
1859D. BOUCICAULT Octoroon I. 13 He don't understand; he speaks a mash up of Indian, French, and Mexican.
The reference to "Octoroon" appears to be for a play called The Octoroon that was first performed in 1859, making the mashup term about 151 years old.
The text was modified to remove a link to http://dictionary.oed.com/cgi/entry/50291914 on September 26th, 2013.
The text was modified to remove a link to http://library.marist.edu/diglib/english/americanliterature/19c-20c%20play%20archive/octoroon-index.htm on September 26th, 2013.