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: 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.