AllMusic writer MacKenzie Wilson said that the song "saunters like classic New Order with its dark-hued mechanical energy."Lost At Sea's Sarah Peters put the track alongside "Public Service Announcement" for showing the band's honed-in musicianship and knowledge of new wave, saying that when they "hit the airwaves, there shouldn't be too many listeners impressed by the band's amount of study - why analyze and appreciate when you could just dance?" Adam Moerder of Pitchfork Media found the track to be one of the few standouts on the record, calling it "one of the few sassy moments on the album, with Endicott mockingly singing in falsetto "Don't look at me that way/ It was an honest mistake."
The video for "An Honest Mistake" was directed by Michael "Mike" Palmieri (Foo Fighters, The Strokes) and features the band performing the song apparently surrounded by a Rube Goldberg machine. The chain starts with several strings of dominoes and includes many other objects, such as light bulbs, eggs, and an aquarium. Different parts of the action are shown from multiple views, often showing it one way, switching to another angle, then switching back to the original view. Eventually a flaming arrow shoots toward a target, but misses to the right.