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.
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 the TIE fighter crashes on Jakku, when Finn searches for Poe in the wreckage he finds Poe's jacket and grabs hold of the jacket arm, but when it cuts to the following shots as the ground starts shaking, Finn's holding the top (neck area) of the jacket, even though it never left his hand.
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.
Continuity mistake: During Rey's lightsaber duel with Kylo Ren, a few shots after Rey does the flip and slices the tree branch, there's a long shot of them in the forest as they're both moving past very distinctive fallen trees around them, and after a few closeups as Kylo keeps advancing on Rey, at the start of the next long shot (right before the chasm first appears behind Rey) they're back to being where they were in the previous long shot.
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.
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.
Continuity mistake: After the Quad Jumper blows up, when Rey, Finn, and BB-8 run to the "garbage" they're running quickly toward the Falcon's forward side - note the cockpit, with its entry ramp lowered and nothing blocking its way, but in the next closeup they're all running from the rear of the Falcon before they rush up its entry ramp.
Continuity mistake: When Rey reaches the top of the ridge and shouts at Teedo, we see there are no footprints in the sand between her and Teedo, so when Rey rushes to BB-8 her lone set of footprints are the only ones behind her in the sand. When Rey walks away from BB-8 telling him "No," there are many more footprints in the sand between her and the droid, even though there should only be the two sets of Rey's footprints - from both coming and going.
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.
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.
Continuity mistake: When Rey returns to her home in the AT-AT she scratches another mark into the wall, and in the next closeup just as she sits down the top part of Rey's outfit is crisscrossed with her left side over the right and her hip bag is at her left side, but after Rey fills her plate and takes her food, she stands up and her top is crisscrossed the opposite way, etc. The first shot is flipped - note the background, compared to the second shot.
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.
Audio problem: Right before Kylo Ren kills Lor San Tekka, he says "You're so right," and the sound of him igniting his lightsaber while raising it upward, then killing Tekka. You can see red light that is flickering at the bottom of the screen while Ren is talking, meaning that the lightsaber is on, but there is no sound of the lightsaber, and there is still a sound of ignition when it is already on.
Continuity mistake: When the imperial officer is informing Kylo Ren that they were unable to find the droid, Kylo slowly turns his head around. In the next shot, from far away, red lighting has appeared on the left side of his mask. The shot cuts back to him and the red lighting on his mask has vanished.