Harry Dunne is a former dog breeder from Rhode Island.
In the beginning, Harry learns that one of Lloyd's taxi passengers Mary Swanson left a mysterious briefcase behind unaware that she was turning in ransom money to get back her kidnapped husband Bobby. Harry is seen being fired from his pet grooming job. He mourns the murder of his pet parrot Petey but thinks that Petey's "head fell off" from old age. Lloyd thinks that life is not cooperating with them and convinces him to leave their clueless lives to Mary's hometown; Aspen Colorado, become friends with Mary and return the briefcase to her.
They get stuck in several obstacles on the way to Aspen Colorado. They are targeted by a mean evil thug named Sea Bass who blames an accident on Harry and soils their food. In revenge Harry and Lloyd trick Sea Bass into paying for their food and other purchased items; and although escaping, Sea Bass vows revenge. Then Lloyd needs to pee really bad and Harry suggests to use bottles of alcohol in their car to urinate in. Lloyd then relieves himself in about 5 bottles. While Lloyd takes care of it, they get pulled over by a snobbish police officer who accuses them to DUI. The officer then grabs a bottle and tries to drink what he believes is beer. Harry and Lloyd try to dissuade him but he tells them to shut up before drinking the urine. Upon drinking it he groans and growls an order to "get the hell out of here!" and as they drive off the officer vomits on the road.
Then they pick up a man named Joe Mental as a hitchhiker. They are unaware that Joe is one of Bobby Swanson's kidnappers who wants the briefcase to give to the primary kidnapper; Joe's life-long friend Nicholas Andre. Mental is frequently annoyed by their stupidity and is forced to suffer annoyances of stuff like their tag wars ending with one of them arguing over whether or not "you can triple stamp a double stamp"; the most annoying sound in the world; and an annoying version of popular song "Mockingbird"
Joe Mental decides to kill Harry and Lloyd with rat poison but changes his mind when he learns that they have no idea on what is in the briefcase. At a restaurant, to drain his annoyance against Harry & Lloyd he puts hot peppers in their food. In retaliation Harry and Lloyd put peppers in his cheeseburger as he makes a phone call unaware that Mental has ulcer problems and thus cannot eat acidic peppers. When Mental lies backwards on the ground dying, he orders them to get his medicine but they end up accidentally giving him the rat poison. Mental then dies of the toxins and Harry and Lloyd flee guilty of killing Mental.
That night Harry and Lloyd learn that they are now wanted by the police as fugitives for Mental's accidental death. As they stop at a gas station, Harry falls in love with a woman that is also moving to Aspen Colorado to get away from her boyfriend. Harry tries to ask her on a date but sets himself on fire by accident. As he burns, he gets impatient with her getting off topic of her phone number, screaming "For God sakes just gimme the damn number!!" Offended, the woman drives off refusing the offer and Harry charges into the bathroom to put out his burning leg and sees Sea Bass lying on the ground KOed and Lloyd sucking his thumb in fear (Sea Bass found Lloyd and tried revenge)
That night Lloyd drives the wrong way running them out of gas. This proves to be luck because if they reached the Colorado border they would have been arrested for killing Mental due to officers tracking them down. The next day they wake up in Lincoln Nebraska in fuel milage drama. Nearly out of gas, they stop on a pullover site. Infuriated with Lloyd for his dimwittedness, Harry decides to walk back to Rhode Island. However Lloyd realizes that the truck is not completely out of gas and drives to a nearby town trading it for an electric scooter. He then catches up with Harry who grows happy with Lloyd for his idea and accompanies him on the electric scooter all the way to Aspen Colorado. In Aspen they are unable to find Mary due to her last name being forgotten.
That night while camping in a blizzard Harry even with a campfire cannot warm his fingers. When Lloyd reveals extra gloves on him, Harry gets enraged that his own friend did not give him extra gloves when it was clear that Harry was freezing. In return for it, Harry tackles Lloyd trying to strangle him, dropping the briefcase opening it to reveal the money.
They decide to use the money to buy their way back to Aspen, a fancy hotel room, a new car, among other posh items and track down their spendings with IOUs. They end up spending every penny of the ransom money and eventually find Mary. Lloyd gets shy and asks Harry to ask Mary on a date for him. Harry agrees but ends up asking Mary for a date for him and her. Harry lies to Lloyd that Mary will come for Lloyd the next day but he really sneaks out of the hotel to attend his date with Mary. On his date, Harry shows his stupidity by licking a frozen flagpole getting his tongue stuck to it; putting a snowman's face in the wrong part of the snowman; among others but Mary thinks it is intentional humor. Eventually Lloyd learns that Harry betrayed him.
Angered with his friend for his treachery, Lloyd pretends to be normal as Harry prepares for another secret date with Mary. While Harry is sprucing himself up Lloyd pours laxatives in Harry's coffee and forces Harry to drink it in a so called toast for their friendship. The laxatives act up while Harry is about to go with Mary on the date. The drink forces Harry to use the Swanson mansion toilet and when he finishes, he finds that the toilet cannot flush. Stuck now with fixing the entire mess, Lloyd uses advantage of this pickle to pick up Mary and take her to the hotel. Eventually Harry figures out that Lloyd did it out of vengeance and decides to go to the hotel to reconcile but is picked up by the woman he shouted at in the Gas Station for an unmentioned reason.
When he arrives he spots Lloyd and Mary handcuffed to the room bed. He finds himself being captured alongside his two buddies by Bobby Swanson's kidnapper Nicholas Andre who is enraged with Harry & Lloyd for spending the ransom. While Nicholas Andre tries to book an escape to Europe, Harry and Lloyd angrily rant over who is in fault for ruining their friendship causing Andre to order them to shut up and decide who is shot first. Harry ultimately decides to take the bullets but survives and retaliates against Nicholas with 5 missed shots from a pistol he somehow got. Then FBI agents rush into the room beating up Nicholas and arresting him. The woman turns out to be an FBI agent who is the leader of the kidnapping case; she used Harry to capture Nicholas and provided Harry the gun; but she shows some antagonism towards Harry when she says that the FBI did not care if he was fatally shot or not but about capturing Nicholas off of it.
Eventually Bobby is reunited with Mary and now with their trip useless and their bought possessions confiscated to pay their IOU debts, Harry and Lloyd decide to wander the earth for jobs unknowingly turning down an offer to become oil boys.
Harry was an incredibly unintelligent man, although he showed signs that he was slightly more intelligent than Lloyd. He was also suprisingly charismatic, as Mary Swanson took quite a shine to him.