For example, if you're teaching integration of $\int \frac{dx}{1+x^2}$, would you mention the common wrong answer of $\ln\left(1+x^2\right)+C$?
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For myself, I very rarely mention common mistakes since I'd feel I'm possibly causing the very problem I'd seek to avoid. But if I do mention issues, I will emphatically state before and after that it's the wrong approach (and often, I'll just write it on at the edge of the board and then promptly erase it so it's not written down by students)
One of the reason why I avoid warning of common mistakes is because I can imagine how a student could see the intuitive appeal in the answer, even though the logic is flawed.