Character mistake: During the debrief meeting with the generals, Roy states the Lima Project was "some 29 years ago" and "the ship disappeared approximately 16 years into the mission." A few minutes later, Roy narrates "I was 16 when he left, 29 when he disappeared." This of course is only 13 years into the mission. (00:11:27 - 00:15:03)
Character mistake: Upon arriving to the house they say Zoe's mother committed suicide when she was 10 but later on before going back to the house to expose her step mom Sam says her mom committed suicide when she was 8. (00:16:56 - 01:17:46)
Character mistake: When Woody Harrelson picks up the movie magazine and opens to a page, he says "I love Clara Bow." The picture he is looking at is of Jean Harlow. (01:00:54)
Character mistake: Toward the end of the film, Detective Davis orders Captain McKenna to put his badge on the table. New York City police always refer to their "shields", not badges.
Character mistake: Detective Spitzer went into Harper's dark/unlit house, saw his partner Greg on the floor, and then saw Alec standing in the kitchen. Without identifying himself, telling Alec to drop his weapon (pistol pointed toward the floor), or bothering to determine what happened, Detective Spitzky shoots Alec. (01:27:08)
Character mistake: In her first walk through the city with Dr. Ido, after feeding the dog her sandwich, Alita takes a flyer and reads it. Between the lines that read "Wanted" and "Murder" there is a line in Spanish that says "Querido para el asesinato." It should say "Querido por el asesinato".
Character mistake: Right at the beginning of the movie, introductory technobabble. "In this canister, there's a solution of protons. The canister is attached to a rotor circuit that generates the protons to the speed of light." I believe the science genius and creator of time travel mixed up the words "generate" and "accelerate" here. (00:00:50)
Character mistake: Nicolas Cage says "first battalion, tenth Marines from Camp Lejeune, North Carolina gunslingers signing out". It was the second Battalion 10th Marines that was called gunslingers, not the first.
Character mistake: Hero asked Judge Straight what should happen to him for killing Ron. The judge replied, "Well, then you should be arrested, incarcerated, indicted, and tried." "Incarceration" is used to refer to long-term confinement of offenders who have been convicted and sentenced. Instead of incarcerated, a judge should know that if a defendant is denied bail (typical for capital crime cases), he would be DETAINED in a jail or detention center while awaiting trial. (00:31:20)
Character mistake: When they're making the protection circle they make a star of David and not a pentagram, 6 points in a star vs 5 points.
Suggested correction: I don't think there was anything in the movie that dictated a pentagram had to be used. In the book of protection rituals they were using, the particular ritual showed a picture of the star of David they needed to create, so that's what they used (plus salt).
To add to the correction, what the mistake refers to as "Star of David" is a hexagram and the use of hexagrams in the occult are not uncommon. You can find salt protection circles that use the hexagram.
Character mistake: There are some musicians at different times in the movie. One of them is playing a moraharpa (traditional Swedish instrument, a predecessor of the nyckelharpa), but holding and playing it incorrectly. (00:38:37 - 01:39:45)
Character mistake: At the start Smith takes a Krestal ballistic computer and barely holds it out to get wind speed. The proper technique is to hold it at arm's length into the wind.