This is really quite hard and somewhat based on opinion.
On one hand he clearly 'tries' to do the right thing but is very misguided in what that is and when corruption is pointed out to him with solid proof he jumps all over it immediately, which would lead you to think he's not corrupt at all, just not the brightest.
On the other hand however, he clearly shows bias to the Preps, meets with Mr. Harrington and demands Galloway to mark Derby up, despite him not performing, if we are to believe Galloway's quote of "Just maybe I'll FAIL Derby Harrington despite of what his father and Dr. Crabblesnitch might say, God knows he deserves it". Then there's all the Jock favourtism as well.
One could argue that Crabblesnitch is doing what is neccessary to keep the school in best condition possible, but based on the fact Bullworth is a bit of a dump except for the Jocks and Preps (on the most part) and he does little to combat the schools actual problems and is almost the entire reason the plot exists, I have to conclude that yes he is indeed corrupt.
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