Dark Wings, Dark Words - S3-E2
Continuity mistake: When Brienne of Tarth is facing off against Jaime Lannister on the bridge, in a shot from behind the blade is angled upwards, not touching her arm, then in the immediate next shot from the front the blade is now lying along her arm.
The Rains of Castamere - S3-E9
Continuity mistake: At the climax of the Red Wedding massacre, Robb crawls towards his dead wife Talisa from the direction of the doors, which are at the opposite side from Walder Frey's throne. Robb turns Talisa onto her back from her left side (ie. he is on the right hand side of her body), and looks down at her face. This means that Talisa is lying in such a way that, if facing Walder's throne, her head is on the right and her feet on the left, towards where Catelyn is holding Walder's wife hostage and pleading for Robb's life. However, when Walder refuses, Robb has changed position and is now on the left side of Talisa's body, which is presumed to be facing the same direction as before as there is no reason for it to have changed. Robb then turns towards Catelyn who is still on the left side of the room (if facing from The Door), and is stabbed by Roose Bolton. As Robb collapses to his death, looking directly at Catelyn, he lands next to Talisa, whose head is now closest to Catelyn with her feet facing the other way, meaning that her body has somehow rotated by 180° in a matter of seconds. This is an especially bad mistake considering that several people have claimed the Red Wedding was completed in one take, which is not possible if this error exists unless Oona Chaplin for some reason decided out of boredom to play spin the bottle with her own body while out of shot, which would have interfered with Richard Madden's position anyway. (00:47:00 - 00:50:00)
The Bear and the Maiden Fair - S3-E7
Continuity mistake: Jamie is getting his stump tended to and some white ointment is rubbed onto it before it is rebandaged. Before the bandage is placed however, the ointment disappears.
Continuity mistake: When the camera pans out from Jon and Ygritte standing on the wall kissing, Tormund and Orell, who were sitting next to them, are nowhere to be seen.
Answer: Basically it's because he broke his vow. A member of the Kingsguard is sworn to protect the king at all costs. Jaime elaborates more on the deed to both Catelyn Stark and Brienne of Tarth, telling Catelyn that no matter what course of action he took, he would be breaking one vow or another (i.e. if he obeyed the king, he would conversely be disobeying his own father), and telling Brienne that the Mad King was planning on burning all of King's Landing, but he did not bother to tell Ned Stark that. Ned Stark felt that killing Aerys was dishonorable and excessive. Robert Baratheon still could have usurped the throne without Aerys being killed.
Phaneron ★