Continuity mistake: Despite having the Phoenix power at the end of X-Men: Apocalypse, which manifests around her as a Phoenix firebird and she uses to defeat the titular villain, Jean Grey doesn't actually get merged with the entity until 9 years later in this movie.
Suggested correction: Jean used her full psychic powers in the previous film, not the Phoenix Force. Even without the Phoenix Force she was an incredibly powerful, Omega Level mutant.
The Phoenix firebird is literally shown to be emerging from Jean's body when she kills Apocalypse. She can't both have the Phoenix firebird already within her and then somehow also have it invade her body in this film. The mistake is valid, and I would argue it should be listed as a plot hole more than a continuity error.
Continuity mistake: In the shot just before the moment when Jean tells Scott "I'll always come back to you", she is shown lowering her hand, which has the thumb under the earlobe. When she does say the sentence, her hand is back up and with the thumb all the way in front of Scott's ear in a very jerky, easy to spot, lack of continuity. (00:21:40)
Continuity mistake: After the "standard medical", Hank takes the heart rate monitor off Jean's left wrist and hand asking her how does she feel. She responds "I feel...good", hand raised, and in the next shot she has again the left hand resting on her tummy. (00:20:35)
Continuity mistake: During the nice big dinner at the house that is going to be taken over by the aliens, the future leader, Margaret, tells her husband she's gonna go check on the dog. The man to her right holds the bottle of wine and gives it a big thumb up as he peruses it. In the reverse shot, he's pouring wine from that bottle with the former thumbs up hand, and back to the original view he's still in the same pose of approval as before, bottle switching hand again. Similar mistake happens when she, now assimilated, comes back: check out of the glasses in the hand of the guys at the table. (00:22:20 - 00:23:45)
Continuity mistake: After Jean kills Raven, she does not have any blood on her before she flies away. She is then shown in the rain trying to wipe away a large blood stain from her shirt in the rain.