In addition to having elaborate maps painted onto the floor for no reason (other than "it looks kinda cool"), Cersei's making a few more changes to the Red Keep in light of her taking over - namely, removing the symbols of the Faith of the Seven and replacing them with the Lannister lion, most prominently seen in the throne room. It makes sense - Cersei literally destroyed the head of the Faith (The High Sparrow), his most devout followers, AND the Faith's most important temple (Baelor's Sept) last season in the most fiery mistrial ever witnessed, and now Cersei is symbolically tearing down the Faith in King's Landing by removing even the symbols.
She made the error of not stamping out the Faith quickly enough once before - she will not make that mistake again. Instead, she'll make a whole bunch of NEW mistakes (like, uh, refusing an alliance with the ONLY person offering you any kind of alliance, even though there's a lady with a massive army and three dragons getting ready to attack you at any moment).
On her 20-mile walk from the beach to the castle at Dragonstone, Daenerys probably noticed a few things - how insanely long the path was, how weird it was that no one was occupying this awesome huge badass (and strategically-important) castle, and how she should really hire someone to clean off the table inside - but something she DIDN'T notice was the MOST IMPORTANT THING IN THE ENTIRE WORLD was right under her nose the entire time.
Not that that's entirely fair to Daenerys - the only reason WE know about the dragonglass mine is because Samwell read it in a forbidden book (in a very poorly-guarded section of the library! Between this and Doctor Strange, there are a lot of secret libraries that are surprisingly easy to break into). There was really no way for Daenerys to have thought about what minerals would be under her ancestral home, or have known how important dragonglass would be for the fight ahead. Heck, she's probably not even fully-updated on the imminent danger posed by the White Walkers. Hopefully Samwell can shoot a raven her way pretty soon and maybe tell her that her old pal Jorah is hanging out in a room and is slowly turning into roast beef.
After Sandor Clegane rescued Arya from being caught up in the Red Wedding, they came across a farmer and his daughter - who offered them food, shelter, and work. And while they gladly accepted the food and the shelter, Sandor decided to brush off the "work" part and just steal the old man's silver and run for it. In his mind, they were weak, and would be dead come winter anyhow.
He was right.
As the Brotherhood approached the small hovel, Clegane was clearly uneasy about the lodging situation and tried to convince the rest to keep moving. But he wouldn't come clean as to the reason he felt nervous about it - after all, these were the people he betrayed and left for dead (they HAD been talking about how bandits were a big problem). And it was much as Sandor had expected - appearing as though the father had killed the daughter and himself to spare them from the suffering of starvation.
At least we can take solace in the fact the father never attempted a top-knot.
It's understood at this point that the show Game of Thrones is very, very further along (plotwise) than the book series its based on - despite the fact that the book series had a decade-plus headstart. And while events in the show won't necessarily the events of the book exactly, it's assumed a lot of the broadstrokes are the same - including the return of The Hound, after suffering a seemingly fatal injury that led to the end of his travels with Arya.
In the books, there is no actual confirmation the Hound survived his injuries and is still a part of the story. As far as we know, he may well be dead and buried...but it's heavily implied in GRRM's A Feast For Crows that Clegane lived: that he was saved by a member of the Faith of the Seven, and is now a novice who serves as a gravedigger on the Quiet Isle. The hints are pretty compelling - the gravedigger is extremely tall, taller than Brienne of Tarth; he walks with a limp (Sandor was last seen with a grievous injury to his leg); his face is covered by a scarf (a necessity - since Sandor Clegane's burned face would be pretty recognizable); and Clegane's horse, Stranger, is being held in a stable on the island.
So it's appropriate that the Hound serves as gravedigger to the farmer and daughter who he left to die. And appropriate that DB Weiss and David Benioff have decided to use this moment to troll the world's most frustratingly slow writer / Jets blogger, George RR Martin.
Sure - WE all have elaborate, overly complex, probably nonsensical fan theories about what's REALLY going on in Game of Thrones (we also may have a few here that would interest you...), but even the characters IN the show can't help but have their own fan theories about the world of Westeros. Namely, what if the sky is blue only because everyone ACTUALLY lives in the blue eye of a giant named "Macumber"?
Sure, Robb Stark and Oberyn Martell dismiss these tales as pure silliness, but the opening White Walker sequence might lend credence to this theory - as we see a giant with a single blue eye...
Is he named "Macumber"? Unconfirmed....for now.