I'm having a slightly similar experience: in that I'm taking a Yang style Tai Chi class for beginners, however I'm not quite a beginner i.e. I previously practised Chen style for a few years with a relatively expert teacher.
Now in this class, I hear the teacher explain the basics, but during that I notice that there are (what I'd consider) some important fundamentals (e.g. to stand up straight), which this teacher never explains.
My question is, does anyone have any advice for me about how to relate to this feeling of lack of teaching on basic Buddhist philosophy when in "class"?
I'm not sure what "how to relate" means as a question, but FYI some of my thoughts during class have been like:
- I don't want to be a guy who argues or interrupts the teacher, shows lack of respect and disrupts class: other students came to learn from him, not to learn from me (see also conceit)
- Occasionally I have added some sentence in my own words, if there's a verbal pause, if the teacher just answered someone's question and seems at a slight loss for what to explain further
- Teachers and students have to start somewhere and maybe you can't teach nor learn everything at once; more time teaching theory would be less time practising, maybe it's his intention to teach barely enough of the static fundamentals so that he can begin to teach the dynamic movements of the form.
- I'm at the class to learn how to practice the (Yang style) form, so as long as I'm getting that (instruction in the form even if not instruction in the fundamentals) I can't complain that me personally isn't getting from the class what I wanted
- It sometimes worries me that other students who are beginners aren't getting enough instruction in the fundamentals (because this teacher isn't teaching everything my previous teacher taught) -- then I think that at my previous class we used to have lessons once a week, but we the students would also choose to meet during the week to practice. I haven't made time here, to do the same this time, but that remains an option: if I were really worried for the other students I could ask to meet them during the week so we could practice the lessons together (without disrupting class).
But what if some of what he says is simply wrong or misleading, would you - in your situation - comment directly on that?
If that were to happen, in my situation I should probably be unsure of myself: because perhaps what he says is one way in which the Yang style that he's teaching is different from the Chen style that I was taught previously.
Also there are few students in our class, so we have every opportunity to ask individual questions. So if he said that we ought to 'something' and I disagreed, I could query that and ask for confirmation, "Is it meant to be like this (demonstrates this) or is it more meant to be like this (demonstrates this)?"
In your case you might (if you wanted to) ask that as a more pointed question, "Is what you just said contradicted by so-and-so who wrote such-and-such?" Perhaps that's an example of a question to ask privately after class, to see whether and how the teacher is able to respond to such a question?
If you're correct in claiming that he said something "wrong or misleading", then what you reply might (if what you say must be "disagreeable") belong to this category of 'right speech' defined in MN 58, i.e.:
 In the case of words that the Tathagata knows to be factual, true, beneficial, but unendearing & disagreeable to others, he has a sense of the proper time for saying them.
(but I think it's worth reading that whole page of 'right speech' guidelines for further insight).
Or perhaps you could find a less confrontational way to say that, e.g. "I previously read so-and-so say such-and-such" without emphasizing that that contradicts the teacher. In general I hope questions are welcome as long as you act towards the teacher as if they're a teacher who you want to learn from. If they say things that contradict your prior knowledge then I hope it's on-topic to ask a sincere question ("can the teacher resolve this contradiction/doubt of yours?"), maybe less OK to make an accusation veiled as a question (e.g. "I know more about this than you do and you're wrong, don't you agree?").