The idea of seemingly accidentally producing a dollar bill with its four quadrants in incorrect positions was first suggested by Howard Lyons in “Money Maker”, published in Ibidem, No. 7, Sep. 1956, p. 22 (in the original journal). Lyons used the old Money Maker roller prop to “print” the comically jumbled bill.
Harry Anderson was the first to use the mismade bill in the context of a Torn and Restored Bill, as recorded as “The Inside-out Bill” in Harry Anderson Wise Guy from the Street to the Screen by Mike Caveney, 1993, p. 116 (this idea, though, was earlier marketed as “The Mismade Dollar Bill” by James Lewis in 1984, with Anderson's permission; see Genii, Vol. 48 No. 5, May 1984, p. 388.) John Lovick, in Switch, 2006, p. 193, adds further details to the history, stating that Anderson made the discovery of the mismade bill independently and long after Lyons did, and created his torn-and-restored routine shortly thereafter, in the late 1970s.