cbwjm
Legend
Well, I've never had it happen that one of my friends kept arguing for the previous ruling after we've corrected the rules and moved on. If they did, then unfortunately that would mean the table wasn't the right fit for them and they would no longer be invited back to play.I'd argue it every time, for two reasons:
1 - if it's that much of an error it should never have been allowed to stand in the first place (i.e. it should have been got right the first time)
2 - inconsistencies like that, where rulings change week to week, wreck the game if allowed to stand and serve to quickly undermine the credibility of the DM. This is why doing so is seen as poor DMing practice. If you're not going to fix the error when it happens, that's fine; but that error then risks becoming a house rule for the rest of that campaign (though some errors are minor enough one could say 'who cares', some others can make enough of a difference in the moment that they do set a precedent).
There is no risk of an error becoming a house rule, unless we look up the actual rule afterwards and decide that isn't how we want to play, otherwise once we know the actual rule we keep using it.
And it isn't like I keep the actual rule from the players to surprise them with it next time, I let everyone know what was wrong and the correct rule for next time. I feel that being able to make mistakes and correct them after the session is important, especially when learning a new game. The ruling keeps the game moving and you better cement the rules on your mind when you look up the rules later.