So I got to go to the premiere and see S4.E01. It's a treat. It moves fast. There is a lot crammed in, but it flows well. This is a brain dump, so I may be slightly out of order, but I'll do my best. I've only listed what I saw on screen, however the significance of certain scenes may be greater for those who have read the books or novellas and I expect discussion will go into further detail, so READ AT YOUR OWN RISK.
At the start, we see Ice being melted down and used to forge two swords. I don't think the names Oathkeeper and Widow's Wail were specifically mentioned. Tywin gives one to Jaime (and tries to order him to quit the Kingsguard, but Jaime isn't having any of that).
There's a scene with Jaime and Joffrey and the Kingsguard book. This scene made it obvious who the book readers were in the audience. Joffrey thumbs through it, noting Arthur Dayne's entry (and mentions the Sword of the Morning) and that there are four pages for Duncan the Tall, who he notes must have been a very impressive knight. He mocks Jaime for having so much blank space under his name.
Tyrion tries to help Sansa, but Sansa doesn't want any part of it. She goes off for some solitude in the godswood and is found by drunk Dontos the Fool. He gives her a piece of jewelry that he says belonged to his mother, with some pretty purplish stones.
Margaery and the Queen of Thorns are picking out jewelry for the wedding when they are approached by Brienne. It's a great moment, Brienne is bracing herself for abuse and instead gets a very complimentary reception from them.
Tyrion goes back to his room and finds Shae waiting and very ready for him. He's not in the mood and she's not happy about it. She brings up diamonds and he starts putting it together that someone tried to get her to leave behind his back.
There's a scene with Jaime and Cersei. Qyburn is just leaving and she thanks him for some unnamed prescription that ended some unnamed symptoms. Jaime asks what that means but she won't tell. He also notices she's drinking a lot more. He starts coming on to her, but she has something in common with Tyrion in that she's not having any of that. She's pissed at Jaime for leaving her alone so long and doesn't take being captured and de-handed as a valid excuse.
Daenerys lines up her soldiers but Grey Worm and New Daario are missing. They're gambling. The bet itself is funny and how Daenerys deals with it is funnier. She starts off not taking any crap from New Daario but he offers her some advice and she warms up a bit. He's smooth, but not annoying so far.
The free folk get some reinforcements. Some very hungry, creepy reinforcements. Styr is... unsettling. They went with both scarification and cannibalism for the Thenns. There's an "eating crow" joke explicitly made.
Jon Snow warns the Night Watch of the impending attack. He explains Halfhand's death and his own oathbreaking.
Arya and the Hound are on the road. This is my favorite part of the episode, they are golden together. Arya wants her own horse. There's an encounter at an inn with someone Arya has run into before, and he still has something she wants back. This part of the episode got not one, but two spontaneous cheers from the audience. It's a brutal fight and Arya gets her Needle back... then returns the favor.
Tyrion and Bronn go to meet the Martell contingent, but the prince isn't there and the other Martells give them the cold shoulder. Instead, Oberyn and his paramour are at the brothel, picking out a girl together. Oberyn also pulls the male attendent into the mix. It's all very sexy... until some jackass in the next room starts singing a damned song about rain. Oberyn barges in to deal with a couple of drunk Lannisters. He doesn't kill anyone, but what he does do establishes him immediately as a badass. Tyrion gets there just a tad too late to prevent all the damage, but takes Oberyn aside. We get the story of what happened to his sister Elia and that he has Gregor Clegane on notice for it.
Daenerys' road trip comes to a halt when they get to a nasty road sign - a dead kid, pointing ahead, to mark each mile.
That's all I can recall right now. I'll do my best to elaborate or answer any questions.
EDIT: added Styr info EDIT: fixed spelling of Oberyn because I figured out why it looked wrong