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)
Revealing mistake: During the duel with the guards, one of the guards has a chance to hit Kylo Ren and Rey, but stops right before hitting them.
Answer: As he says, "let the past die. Kill it, if you have to." Han was his past - he didn't hate his father, but his existence was holding Kylo Ren back from reaching his full potential, or so he believes. The principle is demonstrated earlier in the movie when he can't bring himself to kill Leia, but has no issue with the other TIE pilots blasting the bridge and (he thinks) killing her. He wants to free himself from the shackles of his parents, who cause him such internal conflict. Remove the source of the conflict and he believes he can move on to greater things. Of course, arguably his position is a bit naive, and his actions will actually cause him greater problems down the line.