When Professor Crowley "stabs" the desk with a pencil, there are already dents on it before he starts (presumably from the previous takes.)
The sign on the desk of Dr. Silverstein, Jack Brooks' shrink, misspells "counselor" as "councilor". (Despite various international spellings, a "councilor" is still someone who works for the council, and a "counselor" is someone who counsels.)
The "sodium" the teacher shows is actually dry ice.
When Jack is loosening the union on the pump, he is using the wrench on the wrong part.