It took about a month to complete this particular episode. After filming had begun, BarBara Luna was diagnosed with strep throat. Since the script called for Capt. Kirk to kiss her, they had to postpone the kissing scene for three weeks until she was medically cleared, since they couldn't risk William Shatner getting infected.
In Jerome Bixby's original outline, the Mirror Universe Federation was not evil, but simply backwards in terms of some technology, notably phaser weapons. Initially, Mirror Kirk was to be married to a nurse on board the parallel Enterprise, and Mirror Spock was more Vulcan in temperament. In addition, McCoy's counterpart, and not that of Spock, was to be bearded.
Star Trek was usually not allowed to show women's navels, but Uhura's navel is visible in the mirror universe. Reportedly, this was accomplished by filming while a PA took the Standards representative to lunch. This is a popular myth in Star Trek but it is untrue. By the fall of 1966, the networks had removed this prohibition from their standards. In fact, Star Trek had already done this, as seen at the end of season one's "Shore Leave", when McCoy shows up with two women by his side, both of whom had exposed navels. Besides, Uhura is seen several times with her bare midriff, and they would have never risked the problem of doing this if it meant re-shooting all of the scenes she appeared in.
In the wake of this episode, a group of child fans started a neighborhood-wide letter campaign suggesting that the concept of a "Captain's Woman" be carried over into the series as a whole, and requesting that Stefanie Powers be cast in that role. Eventually Gene Roddenberry's assistant had to write to the group's two "ringleaders," telling them to ask their parents exactly what a "Captain's Woman" was.
To further denote the inverted nature of the parallel universe, phasers are worn upside-down on the left hip.