When Baby is having flashbacks to when he was a kid and his parents were still alive, he can be seen as a child sleeping in bed listening to music through apple Earpods. However, Earpods were first introduced in 2012, and wouldn't have been around when he was that young.
Just before dropping Baby off, Doc turns right on a red light without stopping, and while the crosswalk signal is displaying a "walk" sign. Although one could argue that he is a criminal and is comfortable breaking the law, a criminal mastermind who plans heists knows how not to get caught and would never break two traffic laws in full view of the public (and risk being pulled over).
When the silver Ford Taurus is going into the crusher (after Baby is told to "sunset that ride"), just after the car is dropped into the crusher, the Taurus suddenly becomes a different car (the change is easily noticed by the different door handles), and in one shot, the engine appears to have been removed.
(around 27 min.) As Baby and his gang drive off from their second heist, the camera is momentarily reflected on the Avalanche vehicle. Likewise, the camera crane is reflected on the blue truck - seconds later - as it tries to mow down the gang.
At one point, Buddy refers to a "disabled parking spot". Almost all Americans would call it a handicap spot, while 'disabled' is used in the UK. The mistake is likely due to Edgar Wright, the screenwriter, being British.
During the planning of the second heist, Doc mentions the bank is in Dunwoody, GA, at the top of the "Perimeter" (I-285), and that a possible getaway road is the Buford Highway. Later, Baby and the getaway crew are seen driving south on I-75/85 in downtown Atlanta. None of these highways or locations are anywhere near each other.
Before accelerating away from the post office dock, Baby presses a button to deactivate the passenger side airbag. There is no such button in the Mitsubishi Galant; such switches are only used in two-seat vehicles, not sedans, and may only be used by inserting a vehicle key.
The judge sentences Baby to Federal Prison, but the uniforms in the next scene have the initial s "DOC " (Department of Corrections) which would be in a state level. U. S. Federal prisoners wear khaki colored shirts and pants. Also, Baby wouldn't be washing a police car with state stickers.
In the opening heist, the getaway involves dumping the original car and switching to another. However, while Buddy, Darling and Griff all wear gloves, Baby does not. During his "dance" scene he touches, and leaves fingerprints on, the steering wheel, wiper control, the outside of the door, and a water bottle (which he leaves in the car). During the getaway he also would have left prints on the gearshift and the interior door handle. However, Baby has most likely never been printed therefore his prints would not be in any police records whereas all other heisters indicate they do have criminal records and could be implicated if their prints are found. This is also why Baby is asked to case the post office - he presumably has no criminal record.
During the course of the film, Baby frequently has music playing in his ears in order to drown out the tinnitus (ringing in ear) he suffers. However, most ear specialists recommend people with tinnitus to limit being around loud noises, which would include playing music via earbuds; Baby might being inflicting more damage to his hearing. However, he is also participating in armed robberies, which is not recommended as a healthy cure either.
While planning for the armored car heist, Baby notes that Doc instructed them not to buy their Halloween masks at the same time (to prevent suspicion), yet when they get to the heist JD appears to have picked up all three of the (incorrect) Halloween masks. However, they could easily have ignored the advice as being overprotective or unnecessary.
In the opening car scene, Baby drives a red Subaru between two supposedly identical cars, but several shots of the decoy vehicles (from ground level) reveal VW insignia and a Chevy badge, making it clear the cars are only similar, not identical.
The goof items below may give away important plot points.
During the gun battle with police near the end, Buddy's fully automatic M16 can be clearly seen expending multiple brass casings indicating fully automatic fire. Twice during the battle the sound edit only makes semi-automatic fire (single shot).
Federal prison sentences are given in months, not years. A sitting federal judge would know that and would never made a mistake about it. Also, parole is only possible in the federal penal system after 85% of the sentence has been served, making it impossible for a 25 year sentence to end in parole after 5 years. However, Edgar Wright was questioned about this, and has admitted that there is some deliberate, ambiguous wish-fulfillment fantasy about the ending, and allows that it might be the dream of an about-to-be-executed Baby.
Murder, in most cases, is not a federal crime. So while Baby might not be charged by a federal court, he would face charges under Georgia law for any deaths that occurred during the commission of felony crimes. This would mean the death penalty for him given the numbers and severity of the crimes involved.
He would never get out of prison and he probably would be executed. However, Edgar Wright was questioned about this, and has admitted that there is some deliberate, ambiguous wish-fulfillment fantasy about the ending, and allows that it might be the dream of an about-to-be-executed Baby.