An idiot? Definitely not. "Foolhardy"? Possibly. A novice in the field of espionage? Undoubtedly. Farquhar is willing to do anything he can to help the cause of the Confederacy, and he hopes this spying mission will help him to land a battlefield commission.
... he chafed under the inglorious restraint, longing for the release of his energies, the larger life of the soldier, the opportunity for distinction. That opportunity, he felt, would come, as it comes to all in wartime. Meanwhile he did what he could. No service was too humble for him to perform in the aid of the South, no adventure too perilous for him to undertake if consistent with the character of a civilian who was at heart a soldier...
Spying is a dangerous game, and Farquhar's decision to undertake the burning of the Owl Creek Bridge is not an act of idiocy but one of bravery. His big mistake was not recognizing that the man dressed in Southern garb who provided him with the information about the bridge was in fact a Union soldier--also a spy, and probably a much more experienced one. Farquhar can be blamed for being being gullible and naive, but his actions were of a heroic nature. If successful, he would have helped to restrict Union movements in his home state; instead, he will only be remembered for giving his life in the failed attempt.