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.