Character mistake: Gendry gets declared as Lord Gendry Baratheon of Storm's End by Daenerys. But he refers to himself as Gendry Rivers - the surname given to bastards from the Riverlands. Gendry comes from King's Landing, and bastards from there are called Waters, not Rivers. Given that Gendry is not an acknowledged highborn bastard, he should never have had a surname in the first place.
Character mistake: When Renly and Catelyn are negotiating the terms of Renly's alliance with Robb, Renly calls Moat Cailin "Moat Caitlin." As someone who served as Master of Laws on King Robert's Small Council, he should know the correct name of the territory he is referring to.
Character mistake: When Theon and Yara are given an audience with Daenerys, Tyrion remarks to Theon that when they last saw each other at Winterfell, Theon was making jokes about Tyrion being a dwarf. The mockery was actually the other way around: Tyrion mocked Theon for being a glorified and subservient hostage of the Starks, as well as taking potshots at the foolish strategy of the Greyjoy rebellion.