(at around 42 mins) When Oskar goes to visit his father, his cheek appears untainted, despite the scar and bandage from before. Later, the bandage is back on and even later, the scar appears.
(at around 20 mins) As Oskar shows the Rubik's Cube to Eli, one side is almost completely white, except for one single square. This square changes color between red and blue between shots.
(at around 29 mins) When Oskar finds and inspects the solved Rubik's cube, the camera cuts to a sleeping Eli who is clearly dressed in clothes she won't get until much later in the movie (at around 1h 30 mins), when she picks it from Oskar's mother's closet.
(at around 1h 45 mins) The bully would have had to rotate his arm 180 degrees from the direction in which he'd "normally" hold Oscar's hair, for it to be positioned with his knuckles facing back toward himself, as shown in the underwater shot.
(at around 1h 8 mins) Throughout the movie there is snow everywhere, but it vanishes later in the movie to re-appear again. When Oskar and Eli emerge from the basement, Eli runs across a bridge and eventually climbs up a tree. As she crosses the bridge, snow can be seen in the background, but as she climbs up in the tree there is no snow anywhere nor any traces of it. Next morning, the snow is back and heavily covering everything.
When Eli goes to the hospital, she is told by the Evening Nurse that her "Papa" (Håkan) was on the seventh floor - a secure ward. Since Håkan was brought in by the police for murder and attempted murder and - especially - since he attempted suicide, Håkan would not be able to open his own window from the inside.
In the next-to-last scene, when Eli reaches into the pool to pull Oskar out of the pool, blood can be seen on Eli's hand. No surprise there, but since she just killed the bullies seconds ago, the blood would be fresh and still wet, and would dissolve into the water as soon as her hand went under.
(at around 1h 8 mins) When Eli tells Oskar to go after she licks his blood off the floor, her appearance changes in one shot. This was intentional - Eli is actually portrayed by an older actress in that scene, and also briefly in the later scene where Eli counsels Oskar to be like her when dealing with his bullies. In both scenes she is covered in blood, and the older actress was swapped in to give us a glimpse of who Eli really is: much older than she appears, and driven by a monstrous hunger.
Vampires are not supposed to be able to enter a building without being invited in (as even the title establishes), but Eli was able to burst into the gym swimming pool room herself to rescue Oskar.
There is much vampire lore, some of it contradictory, some of it largely forgotten, and some of it reinvented by the particular author (see the "Twilight" books for heretofore 'unknown' aspects of vampires, as an example). So there is a lot of wiggle room with respect to the 'rules of vampires.' However, with respect to entry into buildings, the rule is generally that 'vampires may enter a HOME only if they have been invited.' Thus, PUBLIC buildings (like a school, or recreation center), caves, or homes/houses that have no current resident, are fully available to them.
There is much vampire lore, some of it contradictory, some of it largely forgotten, and some of it reinvented by the particular author (see the "Twilight" books for heretofore 'unknown' aspects of vampires, as an example). So there is a lot of wiggle room with respect to the 'rules of vampires.' However, with respect to entry into buildings, the rule is generally that 'vampires may enter a HOME only if they have been invited.' Thus, PUBLIC buildings (like a school, or recreation center), caves, or homes/houses that have no current resident, are fully available to them.
At around 13 mins When Oskar and Eli are talking for the first time, Eli asks, "Does there have to be a reason?" The actress says this line too early and momentarily smiles at her mistake, however she quickly regains her composer and says her line.
(at around 16 mins) As Oskar is looking in his clip book with old newspaper articles, a serial number used by the Swedish police is visible. That number ends with 95, which means that crime was committed in 1995. The movie, however, is set in 1982.
(at around 1h 40 mins) The entire crew is visible in the reflection of the glass at the opposite end of the swimming pool hall when the three bullies enter the scene.
(at around 1h 2 mins) When Oskar goes to swing the metal pole "the stick" at Conny he moves his left shoulder back to swing, but instead ends up swinging it with his right.