My professor gave me a module on history that contains several spelling and grammatical errors. Should I tell him about this or just ignore these mistakes?
Many professors are interested in receiving feedback about possible errors in their lecture notes or, more generally, in their course material, albeit they might not be able to amend it immediately.
Since your professor might already know about those errors, ask them politely, e.g. (maybe it's not the best possible phrase, but it's just to get the idea):
Dear Prof. X,
Since I'm currently reading your history module, would it be useful for you if I compile a list of errata?
In this way you should not have any issue, even if they do not care.