On a report Peter B. Parker briefly reads in a flashback, a scathing review for a Spider-Man-inspired restaurant named TGI Spideys begins with, "Spider-Man is New York's hero, it's savior," misspelling "its".
When Peter Parker, Miles Morales and Gwen Stacy are standing outside Aunt May's door, Peter starts walking away until Gwen fires up a web to pull him back. In the very next shot, Peter is back in place but the web behind him is gone entirely.
In the fight between the Spider-Men and the villains at Aunt May's House, Aunt May knocks Tombstone outside with a bat. Seconds later he can be seen briefly in the background fighting in the house again.
When Jefferson is talking to tied up Miles, he references how he can see his shadow moving. However, when Jefferson checks the shadow a second time, the shadow is the same size, despite Miles being up against the door. You can see that Miles shadow is not being cast under the door when the camera cuts to show both sides of the door.
When Spider-Man 2099 first arrives in Earth-67, the police car behind him reads N.Y.P.D. 5087, before the camera cuts to a close-up of the 67 Spider-Man. When it cuts back to 2099 and for the rest of the scene, the police car only says NYPD.
When the Spider-People are transported to Earth-1610, each arrives in a different-colored beam of light and they are scattered in different directions, as shown clearly on screen, making it impossible for them to all have landed in the same spot. However, when recounting the their arrival to Miles, each is shown arriving in a blue beam and they all arrived in Times Square.
When Miles is trying to start writing his paper on "Great Expectations" he is twiddling the pen in the crook of his thumb but when they cut to the reverse angle the pen is between is index and middle finger.
Miles has Gwen's hair stuck to his hand after Gwen's head is shaved to free them. In the next shot, as Miles walks down the hall, his hands are clean. Later, when Miles is confronted by a security guard, the hair is stuck to his hand again.
In Olivia's office, the camera cuts to Miles after Parker asks what he's doing. It reveals he's carrying both the monitor and computer tower. When Olivia says she can't wait to watch Parker suffer in pain, the camera cuts to Miles again, but he's only carrying the tower, not the monitor.
Mary Jane of Miles' universe is shown kissing Spider-Man while hanging upside down on a ladder. However, her hair stays upright and perfectly styled when realistically it should be hanging down towards the ground.
Miles is nearly a foot shorter than Peter Parker, yet when Miles takes one of Peter's old costumes to use as his own, it fits him perfectly. This was done intentionally by the filmmakers, meant as an illustration of Miles' earlier conversation with Stan, the comic shop owner ("It always fits. Eventually."). Miles has grown more confident, more skillful, and more comfortable with his new powers and is finally ready to take on the role of Spider-Man; thus the costume (like the role itself) finally "fits".
Miles' dad lives in Brooklyn, where he gives Miles a ride to school, yet when the villains show up at Aunt May's house, which is in Queens, he picks it up on the radio and drives over. However, it's never said that he is a Brooklyn cop - nothing prevents him from living in Brooklyn and driving a police car there, while working in Queens, especially since PDNY probably serves all the boroughs like NYPD does.
You famously can't unlock the back door of a police car from the inside, yet Miles gets out of his father's squad car unassisted. It is plausible that this is just one of many difference between our Universes. It does make certain sense to give officers the ability to control whether the door can be opened from inside or not, just like in most modern private cars.
Jefferson has what appears to be lieutenant bars on his collar, yet he also has a chevron on his sleeves. If he is a police lieutenant he would not have chevrons as this indicates the rank of corporal. This may be one of the alternate universe's many subtle, quirky differences from ours, e.g. PDNY vs. NYPD.
Miles blames himself for 'being followed' to Aunt May's house, when by then it was public knowledge that May's nephew was Spider-Man (perhaps even earlier, if the brightly glowing, emblem-showing Spider-Cave entry door in the back yard gave it away). However, the villains also knew that they were dealing with entirely different Spider-People and total strangers to aunt May (at least in this dimension), so they wouldn't see a reason to search for these new Spider-People at May's place.
During the final battle Miles takes away Wilson's gun, stating that it would be cheating. If a gun is cheating, then web slinging devices should be too (both are tools used against foes). However, one crucial difference is that a gun is a lethal weapon, while a web slinger is not. Moreover, Miles was obviously joking when he said that (a typical Spider-Man behavior in battle) and didn't seriously intend to introduce any "rule of engagement", if only because evil villains wouldn't accept any such rules and Miles is smart enough to understand that.
The goof items below may give away important plot points.
At the collider fight, Dr. Octopus wraps up Spider-Man with two of her arms, uses one to hang to the ceiling and one to attempt to kill him. In the wide shot when Miles is using her own arm to punch her with it, there's two arms on the ceiling, one wrapping up Peter. When Miles reveals himself it reverts back to two of the arms wrapped around Peter.
When Doc Ock confronts Kingpin at Alchemax and holds the henchman with her tentacles, the henchman points his guns at her. However, there is no way he can see past Kingpin's huge frame to shoot her. She is in no danger of being shot.