Right before Lord Asriel is captured, he slides over a cliff of ice. In the first shot of him when he reaches the bottom at 42:11, he has a large scrape on one side of his face, but in the next and following scenes it is gone.
When Lord Asriel is walking through the snow, before he gets captured, he reaches with his right hand to pull down his goggles at 40:58. In a closer shot also at 40:58, it shows him pulling them off with his left hand.
The first shot of Lyra in the Experimental Station is a reverse angle of her walking through a doorway with double doors at 01:22:35. When the shot changes to the front at 01:22:42, the doors are closed.
When Mrs. Coulter is about to deploy the small robotic bugs to seek out Lyra, she says, "They'll seek her out like bees to honey." Bees do not seek out honey, they seek out the nectar and pollen to make honey. Nonetheless, "like bees to honey" is an old expression based on the affinity of many bees for anything sweet, to which those with an unguarded hummingbird feeder can attest.
Pantalaimon is able to transform into a small moth when he wishes. When he and Lyra are confined in the intercision machine, they are separated by a metal grid through which Pantalaimon in moth form could easily crawl: it is not clear what prevents him from trying this.
The goof item below may give away important plot points.
During the final battle scene, there are a bunch of children attacking a guard. Lyra jumps on his back and then Serafina Pekkala shoots an arrow into the guard while Lyra is still on him. When he falls to the ground the arrow is protruding from his back with Lyra unharmed at 01:37:56.
In the Bolvangar scene, when the children are writing letters to their families, the nurse is walking from table to table when she stops to see Billy not writing anything. In the same shot while the nurse says "Billy Costa-", Roger is next to Billy with his head down (39:03), concentrating on writing his letter. But in the next shot when the nurse says "-why didn't you write anything? Your mother must be missing you terribly" (39:04-39:08), Roger is looking up at the nurse. In the next shot after that while Billy replies, Roger's head is down again (39:08-39:14).