Listen, I don't blame Ed Sheeran for this - if I were a famous musician who had enough pull to get a small cameo in one of the coolest TV shows around, I would do it too. Plus, the actual background of why the producers put him in the show (mostly it was a surprise gift to Maisie Williams, who plays Arya and is a huge Ed Sheeran fan) makes the whole thing kind of sweet. Despite all of this, it was annoying because it immediately jerked you out of the reality of the show - all of a sudden you weren't invested in the Game of Thrones universe, you were watching the dramatic equivalent of an SNL skit with musical guest Ed Sheeran.
Jaime Lannister has - against all odds - become something close to the most normal character on this show, or at least the most rational one. That's a pretty big swing from the self-involved dickhead from the first two seasons, who was casually shoving children out of towers and murdering his cousin out of convenience. But Jaime's arc hit a stumbling block in season 5 (the Dorne stuff) and hasn't really recovered since - and this season found Jaime really afloat and without much character grounding.
What we found out about Jaime during his time with Brienne was that he - seemingly the most dishonorable man in Westeros - was actually one of the most honorable. He had sacrificed his reputation by betraying his oath and stabbing his king, Aerys II, to prevent the Mad King from burning down King's Landing just to spite Robert Baratheon. He gave up his good name and what little honor he had in the eyes of everyone else in the country, and was branded "Kingslayer" - all because he HAD to stop the king from burning down the capital with wildfire.
The previous season ended with Cersei - Jaime's sister - doing EXACTLY THAT. She blew up the Great Sept of Baelor, killed untold amounts of innocents, led to their last child's suicide, and Jaimie responded by....sticking by her? Doing whatever she told him to do? Bringing up the occasional complaint but mostly just following orders and not causing too much of a ruckus? WHAT THE HELL, JAIME?
Okay, Sam, sure - the Maesters are all a bunch of snooty dipshits, you figured out the secret of the dragonglass, AND you figured out the cure for greyscale (turns out it was "literally the first thing anyone would even think to try") - but that does NOT give you an excuse to bitch and moan to Gilly RIGHT AS SHE IS REVEALING THE MOST IMPORTANT SECRET IN THE SHOW (Rhaegar had his marriage to Elia Martell annulled and remarried, meaning it's 99.9% confirmed Jon Snow is his trueborn son and the real heir to the Iron Throne). She lived through Craster and a hell you could never imagine AND she just learned to read - SO BE POLITE AND LISTEN TO HER WHEN SHE'S TRYING TO CONVEY INFORMATION.
Daenerys seemed so noble and pure when she was freeing slaves and burning objectively evil people alive - but since she sailed to Westeros, she's kind of been an annoying asshole: constantly telling Jon Snow that he HAS to "bend the knee" to her, complaining to Tyrion about his poor judgment (as if he could have anticipated Euron's fleet would be able to teleport to Casterly Rock or Jaime could move the entirety of the Lannister forces without any scouts seeing anything), and generally acting like an overly entitled asshole who expects everyone to bow down to her just 'cuz.
The question I don't really get is - WHY does Daenerys want to rule everyone so badly? Wasn't she all about "breaking the wheel" before? Forcing people to bow down to you as their supreme ruler or get ROASTED ALIVE BY DRAGONS seems, uh, NOT PARTICULARLY HEROIC. It seems downright despotic.
Hey, remember when Tyrion was a ribald drunkard who kept squeezing himself out of tough scrapes? That was fun. But, of course, Tyrion grew up and had to take on more responsibilities - which has led to season 6 Tyrion, who is boring as hell, shows no sign of the fun cheeky character we all fell in love with, and seems to be in a dour mood at all times. Of course, things ARE more serious now - he's the Hand of the Queen, the dead are on the march, and everyone on the show seems to be aware the fated end is coming.
But Tyrion WAS the Hand before in doom-filled times (for Joffrey) and he still managed to be fun and cheeky and full of gusto. That seems like a lifetime ago - and now all we get from him are bits of sound advice for Daenerys to ignore in favor of cooking strangers alive.