Other mistake: There's a typo in the end credits - an extra S in "3rd Asssistant." (02:16:30)
Other mistake: When Finn and Rey see Han talking to Ben on the bridge, they look directly down. But the platform they're standing on is to the right of the bridge. If they're looking directly down, they would be looking at either the floor or the chasm around the bridge. They should be looking to their left.
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