Continuity mistake: When Capt. Picard, Data, and Anij are going to the holoship, they start off from the landing dock with (facing them) Data on the left, Capt. Picard on the right and Anij sitting. This is all well and good but after Data opens the door to the holoship, they magically switch places.
Continuity mistake: Picard has a cut on the right side of his head in the scene where he, Worf and Gallatin are on the Son'a bridge. It is most visible when he says to Gallatin "Take us into position". After Picard takes the rifle from Worf and Gallatin says "We're approaching the collector", the cut on Picard's head is gone. After he has beamed over to the collector, the cut is back and is bleeding a lot more than it did before.
Continuity mistake: When Picard and his team beam down to the planet for the first time to "rescue" starfleet officers you see a couple of kids playing a ballgame. These balls were CG, however, in a next shot when Picard is talking to the Ba'ku people you see the kids still playing the game in the background, but without the CG balls.