(at around 1h 15 mins) In the flashback to when Snape and Lily were kids, Lily is shown with brown eyes. This is incorrect because everybody describes Lily to have the same color eyes as Harry in the movie which is blue.
(at around 1h 17 mins) 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 dialogues 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.
(at around 39 mins) 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.
(at around 1h) In the Room of Requirement when Ron is running towards Harry and Hermione he is shown holding his wand in his right hand. However in the next shot he grabs Hermione's hand with the same one. Moments later he is shown to have his wand in his left hand instead now.
(at around 4 mins) When Harry is talking to Griphook at Shell cottage, Griphook states that the sword in Bellatrix LaStrange's vault at Gringotts is a fake, placed there the previous summer. Hermione then asks, "who is the acquaintance?", when Griphook actually made no reference to any acquaintance at all.
When Luna leaves Shell Cottage (to return to Hogwarts), she has long hair blowing in the wind. In the Room of Requirement (when she and Cho talk about Rowena Ravenclaw's lost diadem), her hair is short. When she talks to Harry on the spiral staircase, her hair's long again.
(at around 1h 45 mins) During the battle between Harry and Voldemort in the tower of Hogwarts, Voldemort immobilizes Harry with black strips of cloth from his robes. The movie then cuts to two fights in turn: the first between Hermione and Ron with Negini and the second to one between Molly Weasley and Bellatrix Lestrange. When we get back to Harry and Voldemort Harry is free from the cloth strips which are receding back into Voldemort's robe. How Harry got free is not clear.
The bridge leading away from the entrance courtyard in this movie is shown going straight away from the building from the middle of the wall opposite the building entrance.
In earlier movies, it goes at an angle from one corner.
At the end when Harry and Ginny are taking their children to the Hogwarts Express, Their daughter, Lily Luna Potter can be seen riding James's cart through the barrier and later walking with Ginny through the barrier.
At the start of the epilogue scene a virgin train can be seen at King's Cross station. King's Cross is the southern terminus of the East Coast main line between London and Edinburgh. These trains would actually terminate at nearby London Euston as these trains travel the West Coast mainline between Euston and Glasgow as well to a lesser extent Edinburgh.
(at around 1h 17 mins) During Snape's memory that Harry sees, after Lily is sorted into Gryffindor she, along with the other first years, are seen wearing the same robes and ties that Harry and co. wore during Harry Potter and the Sorcerer's Stone. When she sits at the table and gets introduced to James and (presumably) Sirius on the other side of her, they are both wearing Gryffindor ties and robes. Since they are both suppose to be first years they should be wearing the plain robes instead.
(at around 1h 17 mins) During Snape's memory sequence, when Professor Trelawney is shown giving the prophecy, she is not giving the one that concerns Harry and Voldemort, but rather the one that concerns Peter Pettigrew. Not only is this the incorrect prophecy, but Snape did not hear the prophecy about Pettigrew, so it shouldn't be a memory of his.
In one of Snape's flashbacks he is holding Lily's dead body and she is wearing a light blue button up shirt. In versions of the same scene in previous movies, she is wearing a black turtleneck. This is easily explained as it is Snape's memory that we are seeing, not an objective recounting of the situation. Memories can change subtly over time and Snape may not recall all the details perfectly and may have blended that memory with another of Lily wearing that shirt.
(at around 13 mins) 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.
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. However this is not necessarily incorrect as the limbo scene is in Harry's mind, Harry is also not wearing his glasses because he does not need them.
In Harry Potter and the Deathly Hallows: Part 1, when Harry revisits Godric's Hollow, the entire roof and much of the walls of the upper floor of the Potter home have been destroyed. But in Snape's memory of the aftermath of the attack on the Potters the upper floor is still undamaged. This is because the attack was to kill the Harry to prevent a prophecy coming true, and no damage was done to the house. After their death the house was abandoned and would probably have been vandalised over the years as well as deteriorating until eventually it looked the way it looked when Harry returned to it.
(at around 49 mins) The Parseltongue phrase that Ron uses to open the Chamber of Secrets sounds nothing like what Harry said when he initially opened it. When Harry opened it he at no time is it stated that a specific phrase has to be said in order to open the door, it can be opened by any person capable of speaking Parseltongue.
(at around 1h 12 mins) When Voldemort is calling off the Deatheaters his voice echoes, the echoed phrase "dispose of your dead" comes before he actually says the words. This is because his speech is being communicated directly into the minds of everyone in the battle, not shouted through the halls of the castle. This is evidenced by the sound effects and reactions of several characters just before Voldemort starts speaking. This 'telepathic' type of communication would easily allow echoed phrases to occur before the phrase is spoken almost like a thought occurring before it is spoken.
(at around 48 mins) When Harry is talking to the ghost of Helena Ravenclaw and he moves around her, his shadow is seen on her. As she is a ghost it seems like this shouldn't be possible. Ghosts (theoretically, because they aren't real) do have some physical presence, much like a plume of smoke or dust, which can be seen but also passed through. Shadows would be visible falling upon a ghost.
(at around 54 mins) Just as the bridge collapses under Neville, it looks like he throws his wand forward, but he is just flailing as he begins to fall with the bridge collapsing underneath him. When he later pulls himself up he first tosses the wand onto the floor of the bridge. He never threw his wand away, understandable as he is in the midst of a battle, and this is confirmed by the reverse shot looking towards his startled friends where no wand is visible on the remaining deck of the bridge.
(at around 41 mins) Professor McGonagall speaks the Tabooed name, "Voldemort" BEFORE the protective defensive Charms are spoken; however, Snatchers do not appear. This is because - unlike in the book - Voldemort's name was never confirmed to have been tabooed in the film.
(at around 25 mins) When Voldemort first discovers his Hufflepuff Horcrux is stolen he kills Griphook and the security guards at Malfoy Manor instead of Gringotts. It was never explained or shown how Voldermort's victims ended up in Malfoy Manor.
Rufus Scrimgeour initially claims that the Sword of Gryffindor has gone missing, thereby preventing him from giving it to Harry. Although the sword (actually a replica) was later revealed as having been hidden inside Bellatrix Lestrange's vault at Gringotts, the Death Eaters wouldn't have had access to Hogwarts or the sword at the time of the reading of Dumbledore's will, meaning it should not have been declared missing at that point.
(at around 1h 50 mins) At the end of the film when Harry takes his son to board the Hogwarts Express at Kings Cross, an exterior shot of St Pancras Station is used. St Pancras is a more photogenic building than Kings Cross.
(at around 1h 45 mins) During the confrontation between Molly Weasley and Bellatrix Lestrange it is suggested that two of the spells that Molly casts are actually the same shot reused. All of the spells she casts have different movements to signify the difference between casting different types of curse, trying to get past Bellatrix's ability to block them.
(at around 1h 40 mins) 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.
(at around 1h 22 mins) While we are told that Snape conjured the patronus that led Harry to the Sword of Gryffindor in Harry Potter and the Deathly Hallows: Part 1, he had no way of knowing where the trio were camped. But Harry had the piece of glass that Sirius gave him in Harry Potter and the Order of the Phoenix, which enabled him to see Aberforth Dumbledore. It is possible that Aberforth recognized the area and contacted Snape.
(at around 1h 45 mins) 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. Which is easily explained by the over-protective nature of her family towards her, as Molly steps forward her father and brothers would also act to shield her from harm.
(at around 1h 22 mins) 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 pensieve 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.
(at around 37 mins) When Harry reveals himself to Snape in the Great Hall he is wearing a Hogwarts robe. However his regular clothes are beneath the robe, and he is seen tossing it to the side once Snape flees.
(at around 1h 50 mins) Harry states that the Elder wand never worked for Voldemort because Draco disarmed Dumbledore and Harry disarmed Draco, even though Voldemort "killing" Harry should have transferred its allegiance to him. It's explained in the book, however, that the wand cannot be used to harm its master, and also that Voldemort's defeating Harry was not recognized by the wand as genuine because Harry willingly offered himself to die - thus, it was not a true defeat.