The best lecturer I had in maths would screw up the proofs every time from memory, but the way he screwed them up taught me a lot more than if he'd gotten them right.
I remember a lecturer of mine having to state and prove a theorem due to Heawood[1]. I think he did it first because the statement was quite unpleasant and not easy to memorise. I found the point of proving things from memory is that to memorise a proof, one must distill it to key ideas with obvious steps in between. This was particularly useful if you might need to reproduce a proof in an exam.
My experience is that they get about 45 minutes into the lecture, realize that there was an error in minute 10 and spend the rest of the period trying to fix it before telling you to check the book for the correct proof.
One professor provided scans of his written notes. For one of the theorems in his notes, he’d stated it, attempted to prove it, failed, crossed out the proof and wrote ‘QED’. At least he was honest enough to include it!
