Continuity mistake: As Poe Dameron starts his attack run against the Dreadnought we initially see him from the side and his helmet microphone is folded out to the left away from his face. The camera cuts to directly in front of Poe and the microphone is now folded in and directly in front of his mouth. (00:03:25)
Continuity mistake: When Rey is following Luke upwards the steep terrain, between the two shots in which Luke is visible, there is a shot of Rey kneeling down, following up with her noticing the old Jedi tree. Given the amount of time the camera was focused on Rey, Luke should have been significantly further away as of the second shot in which he is visible. Instead he is seen continuing walking, starting from a point that he had already passed in the previous shot. (There is one dark spot on the ground, in which Luke can be seen walking past to his right in the first shot, which can be used to help identifying the mistake). (00:21:40)
Revealing mistake: After Rey lifts the rocks away from the back exit of the bunker, you can see C3P0 briefly as he bumps into the rock in front of him while exiting the cave, and the rock moves slightly. Also, the rocks that fell over the exit don't match the surrounding terrain at all while piled up as they are smooth like river rocks, but when we see them lifted up by Rey in the subsequent scene, they are rougher and look nothing like they did before (as well as being pretty lousy CGI). (02:16:47)
Other mistake: In Finn's attempted sacrifice, there are plenty of logical inconsistencies. First, Rose's pod is to the side or behind Finn, but manages to beat Finn's pod to the cannon. The collision had a similarly high chance of killing Finn as would ramming the cannon. Finn then carries Rose back to the hideout faster than it took the speeder pods to reach the cannon.
Continuity mistake: During the throne room fight against the red-armoured guards, one of them splits his weapon into 2 blades. In the shot where he gets Rey into an arm lock, the blade in the guard's left hand vanishes from the scene completely, in the middle of a shot. The hand that held the weapon is obscured by Rey's body at the point when the disappearance happens. It could be that the actor dropped it (a strange thing for an elite fighter to do), but then the blade is nowhere to be seen on the floor in the wider shot when Rey kills him.
Plot hole: The entire plot revolves around the First Order chasing the ships, waiting for the Resistance to run out of fuel. They could have easily destroyed the Resistance's fleet by sending a Star Destroyer or two around to cut them off from the other side and blast them into oblivion.
Plot hole: Luke deliberately says he does not want to be found and came to Ach-To to die in The Last Jedi, but The Force Awakens is all about finding a map to Luke Skywalker. Why would Luke leave a map when he never wanted to be found?
Other mistake: Maz Kanata's message is somehow not intercepted by the First Order. It is also projected from various angles and follows her around during her shootout, making one question who is filming the call in the first place?
Plot hole: By having Admiral Holdo perform her infamous hyperspace ramming stunt, Rian Johnson created a continuity problem with the rest of the Star Wars universe. Since this maneuver was successful, every space battle before and since should only include a droid piloting spacecraft ramming enemy bases through hyperspace. This tactic would have been more cost effective and less risky than full on space battles seen in previous films. This tactic would no doubt have been tried in a universe filled with space battles often with disposable troops on both sides, such as in the Clone Wars. The Death Star did not need a successful trench run to be destroyed, just an X-wing with a droid ramming it at hyperspeed.
Continuity mistake: When Poe realises that Holdo is fuelling up the transports, he is suddenly much closer to her than he was in the rest of the scene.
Other mistake: During the big battle between Kylo Ren and Luke Skywalker (as a force projection), Luke appears with his blue lightsaber. While I assume that a force projection probably appear any way he wants, and he did choose to look younger, Luke had lost his blue lightsaber decades ago during his battle with Vader on Bespin Cloud City. He had already built a new green one by the time Return of the Jedi started, so why would he appear with the blue one? It should have immediately given away to Kylo that he was a force projection and not the real Luke.