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.
Continuity mistake: When Sam hands the bureaucrat the letter from Jon Snow, in the shots facing the bureaucrat, the wax seal is on the left side of the envelope (when seen from Sam's perspective). In the shots facing Sam, the seal is on the right side of the envelope.
Continuity mistake: When Jon Snow is all alone in the field drawing his sword to fight the incoming enemy cavalry, behind him we see an empty field. but seconds later as the enemy cavalry is near him they are met by Jon's own cavalry from behind. (00:37:30 - 00:38:20)