George Marshall was slated to direct "Twice Two" and did some pre-production work on the film, but Roach studio management abruptly fired him for falling behind schedule on the previous Laurel & Hardy short, Marchands de poisson (1932). He was replaced by L&H stalwart James Parrott, whose drinking and other personal issues were making him unreliable. He never directed the team again.
It appears that instead of Ollie shaving his mustache to portray his sister, some light-colored material, perhaps makeup, was applied to it to make it disappear; look closely and it's visible.
Second of three films in which Laurel and Hardy play dual roles; the others are Les bons petits diables (1930) and C'est donc ton frère (1936).
The phrase Ollie types at the beginning of the film, "Now is the time for all good men to come to the aid of their party", was a line used as a typing exercise going back to at least 1915. Some later examples substitute "country" for "party".