The film's title is actually a pun. Sara's initial transportation is a mule, that becomes lame, and she trades it for a younger and smaller donkey - which is not technically a mule. So, the second "mule" of the title may be Hogan, whom Sara says "You're as stubborn as my mule." Later, she calls Hogan, "Mr. Mule".
The Finnish title of the film is "Kourallinen dynamiittia", which translates into English as "Fistful of Dynamite". This is actually the alternative English title of dollar-trilogy director Sergio Leone's film Duck, You Sucker (1971).
While Sara operates on Hogan's shoulder wound, he keeps drinking whiskey and mumbling disparate verses from a ballad about a cowboy named Jack Hall who was hanged for burglary in 1701. The lyrics were written in the 1850's by C.W. Ross, a comic minstrel, and are titled "Sam Hall". The last stanza of the song says (which Hogan doesn't sing) - "It's now in Heaven I dwell And it is a ruddy cell: / All the whores are down in Hell, Damn their eyes..." Hogan still believed Sara to be a nun, then.
The cast was headquartered at a magnificent hotel in Cocoyoc for the length of production. Actress Susan Saint James was one visitor to the set. Another Clint girlfriend was reportedly flown in from the Bahamas. Buddies say that Eastwood also entertained at least one lady journalist among the members of the press flown in to tout the forthcoming film.
Don Siegel says in his biography that Shirley McLaine's skin did not fit with the sun, so the production crew hired a female Mexican assistant to stay close to McLaine during the whole outdoors sequences.
Don Siegel said the producer Marty Rackin wanted to save every dollar on the shooting of the movie, and both disagreed on many points. According to Siegel, Rackin used totally unknown and cheap Mexican actors instead of well known supporting American ones.
The trivia item below may give away important plot points.
Shirley MacLaine wrote that since this was filmed in Mexico, it took substantial time to send the film to California for processing and return it for dailies. When MacLaine finally saw the dailies, she was appalled at how overstated her false eyelashes looked, as she was playing a hooker posing as a nun. She regretted that she could not remove them for the rest of the filming because the footage would not match.