> It’s about finding someone who’s not ashamed to fail in front of you—and then figuring out the answers together.

Students aren't going to lose trust in their teacher over mistakes. Establishing core concepts while tripping over details breeds humility for correction when real mistakes are made by the teacher and helps show students that it's okay to make mistakes. This brings more attention to the value of double-checking one's work and the opportunities for correction give purpose to their learning.

Only if you let the mistake go unmentioned. I do a version of this where I glibly include a mistake, like:

    // Examples of dereference operator.
    int i, *ip = ..., **ipp = ...;
    i = *ip; // Assuming ip has been correctly initialized.
    i = **ipp; // Likewise.
    // The address-of operator is the opposite.
    ip = &i;
    ipp = &&i;

I actually talk through the last line. Almost no one ever questions it. I then ask students to look at that last line again, and ask them if an address has an address, and if so, what does that mean, could it ever be useful?

I’d be worried administration thought I had dementia and would be removed.

I read somewhere about a teacher who told his students at the start of each lecture that ONE thing would be wrong.