Deliberate mistake: Despite taking place for at least three years (prior to the arrival of Thomas) in an isolated post-apocalyptic setting, the boys in the Glade have professional looking hairstyles, not the least of which are Minho and Gally, who both have short hairstyles that look evenly cut and professionally maintained.
Continuity mistake: Thomas takes the blade of Theresa at the top of the tower. When he does, his grip on the blade changes position and the hand changes too. (00:55:30)
Continuity mistake: After Minho and Thomas escape from the blades of Section 7, they are crawling through a small passage with the ceiling coming down on them slowly. In one shot, the ceiling is touching Thomas' back. But in the next shot as they get out, he still has a few inches of clearance.
Plot hole: Thomas and Minho decide they are going to go check out Section 7 after they find the creature they killed was from there. But Minho states that when the maze changes, a different section is open every night. Section 7 was open the previous night but they decide the next day that they are going to go to Section 7 to check it out. Then when they get there, Minho is surprised to find Section 7 open and states that it's not supposed to be open for another week...but that's why they went there in the first place.
Suggested correction: That they are surprised by the fact it is open is not a plot hole. They had no other plan, all they had was section 7 and the fact the creature that came from it had died. They theorized something must have changed and they went to check that theory. They didn't know what they would find.
Continuity mistake: When the Griever "drools" on Thomas for the first time, it leaves a big visible trail of drool/slime. Camera cuts and the big visible trail has disappeared instantly. (00:37:00)
Continuity mistake: Ben gets hit round the head with a stick and blood appears. However when they start to carry him to the pit, the blood disappears in some shots. (00:22:30)
Revealing mistake: When Thomas is running through the blades to rejoin the other runner, as they run into each other it is a CGI background. (01:08:50)
Plot hole: At one point it is mentioned that they have tried everything to escape the maze, and that it is impossible to climb up because the ivy doesn't grow all the way to the top of the wall. Yet in the aerial shots the ivy is shown reaching the top of the walls.