In the bathroom scene, Walt says to the dog to give him a break because it's the first time he's ever smoked in the house. Actually, he smoked the night before when Father Janovich was with him inside the house and they also drank beer.
When the Hmong ladies feed Walt in Sue's kitchen, Sue's mother Vu puts a large spoon into a bowl of salad, then moves to transfer the contents to Walt's plate, even though most of the salad fell out of the spoon back into the bowl. Either the actress either didn't notice, or she decided to keep going with the scene.
There is a scene during the reception for Walt's wife, at the house. From the inside, looking through the front door, the sun is seen as shining strongly. However, when they go outside (next scene), it is cloudy.
Walt tells his neighbors that he installed the steering column in his Gran Torino in the factory at Ford. The Gran Torinos of that time were made in Lorain, Ohio. None of the Torino models were ever assembled in any Metro Detroit area Ford plant.
Walt's medical form lists date of birth as February 1930. When his family celebrates his birthday with him, the grass is green, and he joins his neighbors for a cookout. That isn't February in Detroit.
Walt says he used the M1 Garand rifle in Korea. U.S. Military personnel are usually not allowed to keep their service weapons. However, some rifles, identified by serial number, were available for purchase through the Civilian Marksmanship Program after they were deemed obsolete or unfit for service. Enlisted and commissioned personnel also frequently "liberated" their weapons.
The medical form shows Walt's marital status as "married." The film opens with his wife's funeral. It is Walt's first visit to the medical center since his wife died. Based on the conversation with Dr. Chu, it had been more than 3 years since his last visit (long enough that he wasn't aware that his former physician Dr. Feldman had died, and been replaced by her). With all that was going on in his life at the time of that visit, he could have simply forgotten to update his marital status.
While Walt is on the phone with his son, the medical forms show Detroit, and a Michigan ZIP code, but lists the state as California. If you look closely, the California address is Walt's brother, as next of kin.
When Walt touches the little girl's head, the Hmong react very negatively, and Sue tells him that is wrong. Several scenes earlier, Kho Khue patted the baby's head, and no one reacted. Certain elders have the right to touch people on the head, including an elder shaman performing a soul-calling ceremony during a birth celebration. Also, when Sue musses Thao's hair in the back yard, she musses the side of his head, behind his ear, not the top.
In the church, Walt's grandchildren genuflect (kneel briefly and make sign of the cross while facing the altar). In the Catholic religion, the cross is made with the right hand. The granddaughter crosses herself with her left hand. However, the grandchildren were established as disrespectful, both in attire and behavior (one even parodies the spoken prayer), so they could very likely use the wrong hand.
When Walt rescues Sue and Trey from the three thugs, he tells Trey that he should not have said "bro" to them. This would have been impossible for him to know; he pulled up to the stop sign after the incident.
The goof items below may give away important plot points.
Throughout the film, one of the balusters in the railing on the front porch of the Hmong house is missing. At the end, when the brother and sister get into the Checker cab to go to the funeral, the house still has bullet holes and boarded up windows, but the missing baluster reappears.
After Walt punches in his kitchen cabinets and is sitting in the chair smoking, both of his knuckles are bleeding. At one point his right hand appears without blood while his left is still bloody (dried at this point). In another shot of the same scene, where he's talking with the priest, both hands are bloody again.
The gangsters are shown shooting up Thao's house with Mac-10 submachine guns, firing for twelve or thirteen seconds. These weapons are known for their extremely high rate of fire, around 1,200 rounds per minute. The gangsters should have run out of ammunition after around two seconds, or at the very least paused to reload.