Factual error: The main plot is that a teacher answering a student's question about Jesus in a historical context starts a legal firestorm. This is utterly preposterous. Teachers (and students for that matter) are 100% allowed to discuss religion in a historical context. They just can't do things like force other people to take part in religious activities (like prayer) or "endorse" a single religion above all others since public schools need to remain neutral. There'd be literally no case against her.
Factual error: This film portrays the ACLU as being an aggressively anti-Christian agency. This couldn't be further from reality. In the real world, the ACLU would more than likely defend Grace in court for mentioning Jesus in class, as opposed to being the ones representing the prosecution.