When Carl hops on the Ducati in his hospital gown to go see Allison, there is a scene where the back of his gown is open and we can see his butt. But in the next scene, which is shot from farther away, his gown is completely closed in the back.
When the handheld-keyboard player in the band Munchausen by Proxy plays the passage from "The Star-Spangled Banner," the audio plays it in C major, but her fingers on the keyboard play all white keys with the melodic line resolving on an A, following a pattern that would in reality modulate the melody to A minor.
After Carl goes bungee jumping he is seen answering his cellphone while still suspended from the cord. Due to the risk of them falling out of your pocket mid jump, most, if not all, bungee services would advise you to empty your pockets of anything valuable, like a cell phone.
When Carl is singing the song "Jumper" to the man on the ledge, he sings it incorrectly. He sings "And if you never want to see me again, I would understand." The actual lyric is "And if you do not want to see me again, I would understand."
Before Lucy's bridal shower, Carl is checking his messages and listens to one from Rooney explaining he got into a car accident and his car's front bumper is missing. Later after Carl is leaving Stephanie's apartment, his car has it's front bumper.
When Carl arrives at the gas station after running out of gas, the large sign with gas price information shows an unleaded price of over $5, but closer inspection of the gas pump screen shows the unleaded price to be under $3.50.
The position of Allison's arm change after she and Carl take a break to drink water after their morning jog. Her arm with the water bottle can be seen hanging off the rail but then quickly changes position after cutting to a different scene.
In the scene where they travel to Nebraska and attend a football game and their friends see them on TV, the bottom of the screen reads "Nebraska vs. Oklahoma". It should read the other way around; as they were in Lincoln at a home game; the home team appears second.
When Carl's car runs out of gas, he has already turned the car around, so that it was facing downhill. The obvious move had been to simply put the car into neutral (N) and let it ride down the hill to minimize the walking distance to the gas station.
In the scene where Carl is singing and playing guitar to the jumper out of the apartment window, the adjacent window can be seen to have a thick curtain from the outside where it appears to be much thinner from the view inside the apartment. Also, this same adjacent window can be clearly seen from the inside of the room although at times it is blocked off with a solid wall.
The goof items below may give away important plot points.
When Carl is in the hospital and realizes how to reconcile with Allison, he asks the time, and is told "5:40 AM." However, we can clearly see strong daylight illuminating the closed blinds of his hospital room. Then, when he runs outside of the hospital, it is midday. When he arrives at Griffith Observatory, the lighting changes back and forth from midday to early morning.