During the reveal, Shawn says, "all your life people thought you were younger than you look". This would mean that he either looks older than his age or that he acted immature for his years, neither of which would allow him to pass for a teen. Shawn meant to say, "all your life people thought you LOOKed younger than you were." In other words, that he is actually older than he appears.
During the "Phsysics" Lecture, the student incorrectly writes Avogadro's number on the chalkboard as 6.0021415 x 10^23 atoms/mol. When Shawn performs his "reading" on the student, the number is shown correctly written as 6.0221415 x 10^23. When he turns and speaks to the class, it goes back to being incorrectly written. And when Shawn sends the student to the principal's office, it is written correctly.
At the end of the episode, Shawn is playing chess with his dad. Shawn makes a move with his knight putting his dad's king under attack and declares "checkmate". Which would have been legitimate given the surrounding pieces, but just before the credits roll, his dad is about to wipe off the board and the camera shows his dad had a rook on the baseline (H12) putting Shawn's king in check, making Shawn's move illegal. He would have had to move his king out of check before making his knight move.
In a wide-shot of the classroom, Avogadro's number appears scrawled across the chalkboard behind Shawn when he sends a student to the principal's office. In a following close-up of Shawn, Avogadro's number is not behind him on the chalkboard. However, in the next close-up, Avogadro's number is once more visible behind Shawn.