Revealing mistake: While Poe leads the aerial assault on the oscillator, in the closeups of Poe and other X-wing fighter pilots, note the cockpit windows at the pilots' left and right have identical marks and scratches in their individual X-wings. It's particularly noticeable when one closeup follows another.
Continuity mistake: After Rey touches Luke's lightsaber she begins to have the vision, and when she falls to the floor the blaster is missing from the back of her belt, but after she "sees" Luke and R2 and then stands up the blaster is back again, tucked into her belt. (Even though Rey's having her vision of things all around her, she herself is not a vision).
Continuity mistake: After Leia tells Han that she always hated watching him leave and he still drives her crazy, they hug and it cuts to the Starkiller Base. When we see Stormtroopers walking through the corridor and then Rey sneaking away, it's a flipped shot - note the Stormtroopers' backs, and Rey's hip bag and leather wrist cuff. (01:35:15)
Continuity mistake: After Rey finishes her meal beside the foot of the AT-AT and puts on the Rebel flight helmet, there's an overhead wide shot of the toppled AT-AT and we can see its front knee joint. When Rey hears the commotion with BB-8 she rushes to get her staff, which is now tall and upright in the sand at that knee joint, and had her staff been there in the wide shot we would have seen it. (00:14:45)
Revealing mistake: After Poe's X-Wing is destroyed, when BB-8 leaves the village and rolls off note all the distinctive hills and sand dunes in front of BB-8. Later, when Rey hears BB-8 with Teedo and she rushes off note the sand dunes in front of her, but after she rescues BB-8 and walks in the opposite direction those same sand dunes are now in front of them, which were also the same sand dunes in front of BB-8 when he left the village the night before.
Continuity mistake: When Snoke orders, "If what you say about this girl is true, bring her to me," Kylo Ren is wearing his hooded cape. It cuts to Rey restrained in the holding cell, and when it cuts back to Kylo Ren rushing to the holding cell to get Rey and bring her to Snoke his cape is gone. After Rey uses the Force to trick the guard, it cuts back to Kylo Ren arriving at the cell and he's once again wearing his hooded cape. (01:30:40 - 01:31:20)
Continuity mistake: While Finn, Rey, and BB-8 are hiding in the maintenance bay to unfix the poisonous gas, when Finn lifts the floor's slotted deck plate and pokes his head out there are specific grooves at the edge on top of the plate, but no grooves underneath at the edge. The problem occurs when Chewie lifts the deck plate, and those grooves should be on the side facing him (the top side), but instead they're facing out. Then when Han tells Finn "that thing" can understand him, the grooves are gone - the top side of the deck plate is properly facing out. (00:40:05)
Continuity mistake: After the First Order has destroyed the Hosnian system, including Hosnian Prime, Finn rushes up to Han and asks him where Rey is, and when it cuts to the shot of Rey running in the forest it's a flipped shot - note the leather cuff is on Rey's right wrist, etc., then in the next shot the cuff is on her left wrist as it should be. (01:11:05)
Continuity mistake: After BB-8 tells Rey that the Resistance base is located in the Illenium system, while Rey is down in the hold she asks Finn for something she needs and she holds her right arm up and points, but in the shot facing Finn it's her left arm that's up pointing as she repeatedly shouts "NO!" to him, and then it's her right arm up again. (00:38:40)
Continuity mistake: After the Starkiller Base weapon is fired at the Hosnian system, when it cuts to Finn loading gear onto Ithano's ship he stops at the top of the stairs and turns to watch the sky. The blaster's strap is beside Finn's neck slung crossbody, but in the shot from behind there's no strap near his neck. (01:10:20)
Continuity mistake: After the spy, Bazine, communicates that she's found the droid at Maz Kanata's, in the following side closeup of Kylo Ren we have a good view of the distinctive surface dents/hole on the side of his mask (his left side) and this is a flipped shot, then in the front closeup of Ren those dents/hole are now on the opposite side of his mask with different marks the other side. (00:58:55)
Other mistake: There's a typo in the end credits - an extra S in "3rd Asssistant." (02:16:30)