While Harry is running through Snape's memory a scene from the book is presented. It is about when Snape is still a death eater and listens secretly to the prophecy made by Sybil. However Sybil from Snape's memory is shown making a different prophecy. It is the prophecy made by Sybil in Prisoner of Azkaban. Not only the scene but also the dialogs are wrong.
When Harry and the characters are in Gringotts, they go through a waterfall. After they have fallen out the cart, Hermione gets up, wet, but the next time you see her she is dry (her skin and clothes don't reflect light as much as they did in the previous shot), then in the next shot, she is wet again.
When the trio change clothes after jumping into the black lake, Harry puts on a long sleeved shirt that is gray with a dark collar. Later, in the "limbo" scene, he is shown wearing the same gray shirt with dark collar but short sleeves.
When in the Great Hall where Pansy Parkinson is pointing out for somebody to grab Harry and when his friends starts gathering closer to him, Ron is nowhere to be seen for the entire duration of the scene in any of the people surrounding Harry.
In Harry Potter and the Deathly Hallows: Part 1 it was established that the trio had gained control of Bellatrix Lestrange's wand at Malfoy Manor. However in Part 2's Gringotts lobby scene, Hermione-impersonated Bellatrix refuses to show her wand as ID. In the movie Griphook can be heard whispering "They know. They know she's an impostor. They've been warned", so obviously the request for the wand was unexpected even to him. It's thus pretty safe to conclude that the real Bellatrix had reported her wand stolen and alerted Gringotts prior to the trio's attempted break in.
The goof items below may give away important plot points.
When Bellatrix casts her spell at Ginny in the Great Hall near the end of the film, Ginny is standing in front of her family. However, when Molly Weasley comes forward to attack Bellatrix, Ginny is suddenly behind her father and brothers.
When Harry is viewing Snape's memory, he sees Dumbledore with Snape, as Snape casts the patronus charm. This is not the same patronus that leads Harry to finding the sword of Gryffindor in Harry Potter and the Deathly Hallows: Part 1, it is merely to highlight to Dumbledore the extent of his love for Lily.
When Lily and James are pictured as they are murdered both in Harry Potter and the Sorcerer's Stone and in Snape's penseive they are wearing different clothing than when Harry uses the Resurrection Stone so that he may have them with him as he dies. The resurrection stone does not always give those brought back the same appearance as when they died.
When Draco returns to his parents (after Voldemort hugs him) he is seen to be leaving in the crowd with Narcissa. In the next shot, he and his mother are still standing in front of the crowd/behind Voldemort. However, Draco and Narcissa didn't actually leave the crowd... they are seen stopping and turning just as the scene cuts to Neville as he is about to step forward. The Malfoys didn't actually leave until Neville pulled the Sword of Gryffindor out of the Sorting Hat and Harry drops from Hagrid's arms, alive.
The first spell (i.e. wand movement) Molly Weasley fires at Bellatrix Lestrange is exactly the same as the second time she fires at Bellatrix (after Bellatrix attacks her and laughs). They re-used the same shot, the only difference is the colour of the spell.