Continuity mistake: The position of Alita's hands on Hugo's face changes between shots a few times as she holds him in the church. (01:38:55 - 01:39:40)
Continuity mistake: The hair on the severed head under Alita's arm changes arrangement between shots. (01:41:00)
Continuity mistake: In the battle with Grewishka and the other two murderous cyborgs, Ido loses his scythe that falls down with the sharp edge pointed towards his right. When Nyssiana disrobes, though, the scythe is turned the other way incorrectly, with the pointy end on the opposite side and the burner on the right. (00:28:15 - 00:29:00)
Continuity mistake: After Alita slides away from the Centurion, dog in hand, she freezes in the pose at the side of the road. To her left, witnessing the scene there's a woman wearing sandals and some rasta patterned pants. She is standing by the corner of the sidewalk, but when we see her after a brief reaction shot on Hugo, she is standing super close, literally in Alita's shadow (they both shifted away from the corner, technically). (00:11:15)
Continuity mistake: During the whole sequence when Alita wakes up in bed, in the closer shots the blanket directly by her pelvis is on top of the mattress, while in the shots from a wider angle part of the blanket dangles off the side. (00:04:00)
Continuity mistake: Alita just woke up at the beginning of the movie. When she sneaks downstairs checking out of the unfamiliar location, she suddenly has her hand on the railing between shots. (00:05:30)