As with any position of power, responsibility is bestowed onto a GM when running a game. Because good GMing has a lot of impact on overall enjoyment, the GM carries a certain amount of weight behind his rulings and decisions, both mechanical and narrative.
However, sometimes the GM is not the most experienced, smartest or even observant person at the table. In those cases players are requested to up their suspension of disbelief for the good of the game. As some RPG experts describe it, any new group and any new GM should be given a certain credit of trust and use it to introduce entertaining challenges and interesting stories into the game without being questioned.
However, sometimes the group does not give enough trust or time for that effort to pay off, or they might have a hard time divorcing themselves from their (higher than met) expectations. In those cases the GM might be up against subversive behaviours. Most common is rule lawyering, especially if there are players better versed in the game systems than the GM, which is dealt with in a different question. Sometimes, however, narrative decisions are being challenged and from time to time the players are logically, objectively right.
To give an example, if the GM establishes a certain magical disease leaves no one alive and then forgets that a character has been previously infected, it is possible that the players point out that the character is either special in some way (immune, shielded etc. and it has been established the character is not) or should be dead. This is a classic "Oh c***" moment and with a nice group it is jut pointed out and the group moves on. However, sometimes a player will get hung up on that detail, demanding explanation, convincing another players that there is a better way of driving the story or even make an argument about how uninformed the GM is for committing such a mistake. In fact in my previous experiences, it didn't take much for some players to start narration-lawyering, especially in modern or historical settings. To put that into perspective, one player argued with me about how the middle-eastern characters in my 15th century carry the wrong kind of knife, as well as pointing out certain anachronisms regarding military tactics and science.
The GM himself might be frustrated and reluctant to experiment when it happens. Of course, one can brush it off as "yeah, you're right" and do a quick retcon, but it doesn't seem like a good long term strategy. One could as well use his assumed authority and go "It's how it is, because I say so" or even try to re-write parts of the narrative to fit his blooper, which might change the narrative goal of the story and throw the game off the rails.
These behaviours, to some degree, will always be present in new groups in their storming phase, where players test the boundaries of the social contract and the game, likely without ill intentions. However, I'd like to know how does the GM react to such challenges without hampering his future narrative potential?