In the season's finale Sam finally reaches the Citadel announcing he came by order of Lord Commander Jon Snow. The guy at the Citadel was unaware that Jeor Mormont wasn't Lord Commander anymore. The news of Jon Snow becoming Lord Commander seemed to spread to other parts to Westeros I believe probably because of ravens and/or messengers and judging by all the events that happened after Mormont's death many months would have passed, maybe even more than a year. Therefore I find it very hard to believe that that news hadn't reached the Citadel yet. Is there an explanation for this?
I think the answer comes from the interaction they show and with the fact that Sam telling the person looking at the books that news causes that individual to be very non-plussed because the notification is "irregular." He does not even write in the new Lord Commander, just crossing out the old ones because they are dead, leaving it to someone at the top of the bureaucracy food chain to figure out how to deal with events that aren't exactly in order.
It looks like the citadel has a very specific way of updating their official records, so "word on the street" would not be sufficient for them to change their records.
Maester Aemon mentioning the demise of Lord Mormont in the letters would not be a flaw, necessarily, because he wouldn't have sent one of those letters to the citadel, because they wouldn't have troops/bodies to send to the Watch, and it is the sending of these missives that occupied his time between the new Lord Commander taking over and his untimely demise, as referenced by Sam. It also seems like the citadel is a bit removed from the real world, looking like they literally live in an isolated "ivory tower."