theBSDude

In the main series, Mami is the only magical girl operating in Mitakihara, and that immediately is in conflict with the events of Nagisa's Wish where Inui is a local magical girl and Yuu is passing through town. Mami also isn't mentioned at all in the event until the very end after everyone is gone when Kyubey decides to enlist her for cleanup, and that is in conflict with the main series where Mami was unaware of Charlotte until Madoka went to find her.

One of Kyubey's tactics for entrapping Nagisa involved asking Inui to take on a mentor role, which she initially agreed to until she saw how young Nagisa was and backed off. When this happened, Kyubey didn't pivot to asking anyone else to take on that role, which is odd if Mami is also around.

My thought is that Nagisa's Wish takes place a few years prior to the main series back when Mami was still a rookie and still fresh from her family's accident, not equipped for a mentor role. Inui was the primary magical girl of the territory at that point and when Kyubey enlists Mami for cleanup at the end after Inui became Urhmann, Nagisa became Charlotte, and Yuu fled, that was Mami being promoted to become the new boss of the area in the wake of the power vacuum.

Charlotte's appearance in episode three is odd because she's the only witch I can think of that showed up as a grief seed first before hatching into a witch. When Sayaka transforms it's a direct transformation from Sayaka into Oktavia with the soul gem converting into grief seed at the same time, and when Madoka became Gretchen we saw something similar occur. Witches are capable of hatching out of the grief seed again if it's not disposed of properly, and by properly that means giving it to Kyubey, but this doesn't seem to occur on their first manifestation, just as a thing that can happen to make them reappear later. I don't think Charlotte's grief seed in episode three could have been the immediate aftermath of Nagisa transforming in the hospital; it seems more likely to me that Kyubey just left it there as a trap for Madoka after being given the grief seed for disposal a couple years prior.