Character mistake: When the elder Vulcans inform young Spock of the death of the older Spock, they show him a tablet that has him listed as "Second Officer - USS Enterprise." Spock was First Officer.
Other mistake: When the saucer of the Enterprise finally crashes, all sorts of dust comes into the bridge through the big window at the front. Two mistakes here: 1. The very next shot shows that the dust cloud never actually reaches up to the bridge (which is in the middle of the saucer) and 2. Later in the movie, Kirk and Chekov escape the bridge, but to do so, they need to shoot the window out. So the dust couldn't have got in even if it had reached the bridge. Which it didn't. (00:32:25 - 00:51:30)
Suggested correction: The dust and debris seen isn't from hitting the dirt or ground. It came before when the saucer was crashing through the mountains and you see the entire top of the saucer covered in dust. But the debris didn't have to come from a window that was later shot out. It could have come from other widows or hull breaches, not to mention the fact that what we see is probably the interior of the ship itself.
Continuity mistake: During Kirk's birthday party at the end, Scotty's hair is a different style and colour than the rest of the film. He also has a beard, but there is no time for him to have grown one since this is supposed to be a few days after the battle with Krall.
Other mistake: When Krall boards the Enterprise, he lands his ship in the top of the saucer, but then later, Uhura separates the saucer from the neck of the ship with both her and Krall still inside it. And then when they are back on the planet's surface, they arrive there in Krall's very recognizable three-nacelled ship, whereas all of the other ships from that fleet only have two nacelles.
Suggested correction: The other ships were also taking Enterprise crew members, so there's no reason to think whoever was left to pilot Krall's ship couldn't pick up Krall and Uhura.
