When Auggie's dad drags the Christmas tree out of the house the tree is in the first two shots held by the bottom, in the third shot when the tree is almost through the door the tree is held by the top.
After the first scene of Auggie in Mr. Browne's 5th grade class (at 0:18:54), the film cuts to a blackboard in the Pullman home showing an algebraic problem of two equations in two unknowns: 3X + 2Y = -4 and 2X + 3Y = 4. The solution to this problem is X = -4 and Y = 4. The solution shown on the blackboard, X = 3 and Y = 3, appears to the the solution of the two equations 3X - Y = 6 and 2X + Y = 9.
After the fight between the five Beecher Prep boys and the two seventh grade bullies at the Pennsylvania retreat (at 1:36:35), as Henry says "They were huge!", he throws both arms up, lifting his sweatshirt to reveal the black cord to his microphone.