While filming the scene where Picard, Riker and Worf investigate the fire in the cargo bay set by the Irish settlers so they could cook, Patrick Stewart found the dialogue so hilarious that he started laughing uncontrollably, and forced himself to turn his back to the camera to continue. With cameras still rolling, Jonathan Frakes approached him in-character as Riker, and Stewart, still laughing, turned back around and improvised the line about bowing to the absurd.
The title is part of the traditional Irish expression "Up the long ladder and down the short rope", i.e. being executed by hanging.
Colm Meaney (Transporter Chief Miles Edward O'Brien) was reportedly not too thrilled by the story's depiction of Irish characters. Being little more than a bit player, he had no say in scripts. Years later, in If Wishes Were Horses (1993), Meaney was a series regular, and was given a script focusing on O'Brien's Irishness in a condescending way. He had the "Wishes" story rewritten to eliminate, or at least mitigate, that slant.
Writer Melinda M. Snodgrass received a lot of hate mail from the right-to-life crowd for Riker's line, "I have the right to control my body."
Geordi explains to Riker and Pulaski that his VISOR can act as a lie detector, by revealing physiological changes in a human who is lying. This ability is never mentioned in any other episode.