It seems that - like so many things - policing for arguments with fallacies exists on a spectrum:
At one end we have "no policing for fallacies": This strategy makes you an easy mark and wastes a lot of time.
At the far end you can become a pedant, and needlessly derail well-intended, reasonably logical discussions.
It seems there ought to be some sort of useful 80/20 rules, or rules of thumb for the correct use of fallacy policing.
For example, I'm trying to get skilled at spotting false dichotomies. (e.g. "you're either with us or you're against us"). It seems to me that if I'm watching a debate or reading an article, and the speaker bases his argument on a false dichotomy, I can comfortably move on - no need to waste time. This might be a useful moderation technique, if used compassionately, e.g.:
"Bob, we shut down arguments that are based on false dichotomies, come back and start again when your argument has a solid foundation"
Spot false dilemmas now, ask me how!
(If you're not on the edge, you're taking up too much room.)