Corrected entry: It would have been extremely rare for Christian males to be circumcised during the time period of this film. Since David and his family are practising Jews, he would have been circumcised. Since all the boys at the school shower in a big group shower, they would have known and/or suspected David was Jewish from day one.
Corrected entry: When Mr. Gierasch finds Charlie's cheat sheet on the floor he apparently has no idea who it belongs to, but he could have simply compared the handwriting on it to the handwriting on all of the students' exams - whichever exam matched the handwriting on the cheat sheet would have immediately exposed the cheater (Charlie). Mr. Gierasch would certainly have been intelligent enough to think of doing that as opposed to the way the sequence plays out only to benefit the movie's plot.
Correction: We see during the student meeting that Gierasch told them it was block printed. Charlie intentionally disguised his writing in case he was caught.
Correction: In the US at this time, particularly in the milieu of this film, it would have been very common for Christian males to be circumcised, even more so than today, when circumcision is still common in the States.