Continuity mistake: When Rey unloads the net filled with parts at Niima Outpost, as she picks up her staff to her right we see the black bag hanging on the side of the speeder (note the bag's straps are now much shorter than when she drove off on the speeder), but in the next shot as she continues to pick up her staff, which is now to her left, the black bag is suddenly gone from the speeder (when Rey pulls the net it looks as if the black bag is lying in the net with the parts, though she didn't put it in there), and the net is entirely unattached as well. (00:12:40)
Continuity mistake: During the exchange between Ray and Solo note the compressor she is holding. The wires are at the top, next shot these are at the bottom, then they are back at the top, and in the last shot the wires are gone. (00:51:55)
Trivia: Harriet Walter, who appears as a Resistance doctor treating injuries Chewie suffers, is the niece of Christopher Lee, who played Count Dooku in Attack of the Clones and Revenge of the Sith.
Continuity mistake: When Finn asks Rey if she can unfix the poisonous gas they rush to get the air masks, and as Finn climbs down to the maintenance bay below deck we see the floor behind Rey when she starts to kneel to help BB-8. Then after the closeup of Rey helping BB-8, in the next shot as Finn takes BB-8 from Rey we see the corner of the floor's deck plate that has suddenly appeared behind Rey, which she reaches for in the following shot to cover the maintenance bay. (00:39:45)
Trivia: A model of the tumbler from The Dark Knight trilogy is spray painted on the white hull of the Millennium Falcon, and mounted to its underside. This is because there was a friendly competition between JJ Abrams and Zack Snyder to see who could one-up the other by putting Batman/Superman references in Star Wars and vice versa.
Trivia: Unkar Plutt, who Rey sells her haul to, is played by Simon Pegg.
Trivia: In Rey's force vision, before she sees R2-D2 and Luke's robot hand, she runs down a hallway - the same one from The Empire Strikes Back during the final lightsaber duel between Luke and Darth Vader. This sequence was originally going to be longer, with her seeing the duel itself from a new perspective (one of the reasons Darth Vader is one of the Force Awakens toys).
Answer: The First Order already has the piece that R2-D2 was carrying as well. That is the first piece, the large piece of the map missing a small section. The second piece is carried by BB-8 and only by BB-8, the missing piece in the map. All the first order needs is that second piece, and so does the Resistance. However the Resistance needs R2-D2 to activate again so he can show them the first piece, so they can put the second piece in it.
lionhead