I'm psyched about the 7th season of the show, and this question just occurred to me unbidden. I hope it's appropriate for r/AskHistorians. I will go peaceably if not.
Oh, were to start...
Everything and everyone is bleak and more often than not filthy- dirty, because that what medieval period was, according to Hollywood
Taverns taken directly from D&D (inspired by establishments that came around in about 17th century)
Mountain and Viper duel (parity of opponents equipment is kinda the entire point of having a duel)
War have way to many battles (albeit, to be fair GRRM did a good job justifying it)- even notable commanders like Edward the Black Prince or Richard Lionheart had 2-3 "real" battles.. in they lifetime. Entire campaigns could go without a single battle. Sieges was the way of medieval warfare.
Peoples have way to many clothing (even rich had very little in comparison to modern days)
Same goes for the food.
God-dammed torches everywhere and on everything.
... and so on.
On the the other hand, the setting really is a mess of different periods and regions: we have viking-ish Iron islanders, fully High Medieval Reach, pseudo-Moors in Dorne and Renaissance Italian city states stand-ins in Essos.
Many things that would be normal in one is entirely out of place in another but in general neither books or series gives a realistic depiction of medieval period (or some more specific time/place) and relies rather heavily on established tropes and stereotypes.
Adding to /u/Pseudohistorian's list I would add the lack of farmland, around cities and just in general. All usable land would be used for farming especially near the cities because that is where, you know, they needed food.
Around King's Landing 1 2, you only have forrest. Yes I know you can have orchards but that doesn't seem to be the case because it looks just like a normal forest with different trees. Why would the biggest city in Westeros not use the land around it for food production?
An even better example of this mistake is Winterfell 1 2, it's all grass and in some other scenes there is forest. It looks like there are miles of grasslands that noone is using.
Look in this thread from a few months ago in /r/history, it's mostly cities from after the middle ages but there are still a few in there. There is a mix of historical and more recent images/reconstructions of cities and pretty much all of them include farms right up to or even inside the city walls.
