Factual error: In the scene where St Matthews is Playing St Luke's in Football you can ADAMS printed on the chin strap of Matt Damon's Helmet. This movie was set back in the 40's or 50's and Adam's was not making those chin straps especially with ADAMS printed on the strap for many years to come.
Other mistake: 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.
Continuity mistake: After they find out that David is Jewish, he goes to his room and finds a sign. He posts a note on the wall challenging the person who made the sign and when the camera angle zooms in on the note, the note is seen posted at a different angle then when he first posted it.