Filling in gaps in lecturer's instruction I am studying a Honours level Reading Unit.
A Reading Unit is quiet unlike the traditional be lectured to type units.
It is based on the principle that everyone in the unit has mastered how to do research, and that teaching is the best way to learn.
Over the unit there are a number of areas to be examined.
For the first half of the unit the class is broken up into groups one group for each area, and ask to research and present on the topic.
(The second half is a project, and ensuring you know all the areas covered for the exam)

The unit has 5 hours of content lectures, in which it described the basics of all the topics, so that everyone has some context to start there research in.

In one particular topic area, the free lecturer admitted that he was less informed about it, than the other areas covered by the unit. Which is fair enough -- he was asked to teach this class with short notice after the normal lecturer went away. 

I am well informed on this particular topic -- at least to the extent it will be covered in this unit. It forms basic knowledge that underlies my honours thesis, and I have studied a unit though a online university purely about it. I have made the lecturer is aware of this.

During the lecture on the basics of this area, I felt that there were some improvements that could be made to what/how it was covered:


A few times the lecturer hedged his statements. Saying things like "I think that...", "It is my understanding that", "I don't believe anyone does ...". Indicating his own uncertainty. I could confirm that he was right, or clarify this.
A few times he used a term that no one with in the field would use to describe the technique; because that term is used in-field to describe a different technique. It was a very apt way to describe it, but if anyone tries to research the term, they will get this other technique. As well, if anyone every tried to discuss it with a researcher in the field, that researcher would probably say: "no it isn't X, it is Y". (Infact Y uses lowercase x)
A statement in one of the slides was slightly misleading.


I resisted the urge to clarify him during the lecture, because I felt that would be disrespectful and would interrupt the flow of the class -- which was already on a tight scheduled. 



Now I am considering what I should do. Options I see are:


Do nothing, hope that the students covering this section in more detail will make it clear for everyone.
Pass this information on the students covering the area, possibly also with some other useful recommended reading.
Post my clarifications on the the units online discussion forum.
Email the lecturer saying: "I feel I can clarify a few things", shall I post to the discussion forum? But not include full details in my email to him.
Email the lecturer saying: "Here are some clarifications of the area for your edification."


What is the correct way to go about making something more clear,
 that was not wrong, but might be missing or misleading from lecture content?
Remember that this is a postgraduate degree. The lecturers aren't there to serve it to you on a plate. You are a grown-up now, you're doing a higher degree. That means you should be expecting to do most of the work for yourselves, and to think for yourselves.

As there's an online course discussion forum, that seems like the perfect place to work with other students to fill out the richer tapestry of knowledge that the lecture was on; post something there about useful key terms to find relevant literature, along the lines of the following:


  I found these papers (give linked DOI or other robust form of link) on the Dunning-Kruger effect. My search terms to find them were: "cognitive bias", "self-assessment". I looked in these databases / used these search engines.


Fill in gaps. Don't try to look smarter than the lecturer. It's not at all likeable, and you're only risking looking foolish later.

So if the lecturer talked about solving a particular problem by applying X, and you've found examples of people doing it by applying Y, say just that. If you can link to a paper that compares X and Y, even better.

Please do bear in mind that the presence or absence of expressions of uncertainty ("I think that ...", "I don't believe that") do indeed often mark the difference between expertise and weak knowledge. But in the opposite way round to the direction you might think. Presence of expressions of uncertainty often indicate deeper knowledge and expertise. The person who says to fellow academics "I am sure that ...", "I know for a fact that ...", "No one in the world tries to tackle it this way ..." is often, in doing so, flagging up their own lack of expertise.

And yes, all lecturers are mortal, and not every statement they make will be accurate. And that's alright. A degree is an exercise in learning to think, at least as much as in acquiring knowledge. Develop your critical thinking on all materials provided to you, whether they are written, spoken or however they're delivered.