The title, "Valar Morghulis," means "all men must die" in High Valyrian. It is a customary saying in Essos, and is traditionally answered with "Valar Dohaeris" ("all men must serve"), which is also the title of the next episode (Valar Dohaeris (2013)).
The showrunners played a practical joke on Alfie Allen by sending him a fake script where his character Theon was killed by the crippled Bran, in the hope of getting an angry response from him. However, when Allen responded quite favorably, they decided to go with it for a while. Only when they told him that they were planning to bring him back as an undead wight did Allen realize that he was being pranked.
The fight scene between Jon and Qhorin was filmed on a cliff with a 500 foot drop, and took 2 days to shoot. Due to the thick layer of snow in which their feet were sinking all the time, both were exhausted afterwards. In the books, Qhorin attacks Jon at the mouth of a cave, almost immediately after both were caught by the wildlings. Ghost has accompanied Jon during his infiltration mission, and attacks Qhorin, almost tearing his leg off, which allows Jon to kill Qhorin. Qhorin's last words aren't "We are the watchers on the Wall," but "...sharp."
When Pycelle gloats over Tyrion's demotion as Hand of the King, he assumes a normal posture and speaking cadence, showing that his usual frail constitution and absent-mindedness are merely a show that he puts on. In a scene deleted from season 3, Tywin sees through the ruse, and Pycelle admits that he keeps up a charade of weakness so that he appears harmless, and no threat to anyone.
During the sack of Xaro Xhoan Daxos' palace, Jorah Mormont (Iain Glen) says a Dothraki line that is subtitled as "take all the gold and jewels!" In reality, the line was improvised because the crew couldn't get a hold of series' language consultant David J. Peterson. Glen just said something that sounded vaguely like Dothraki. Peterson later re-translated the Dothraki line as "the remaining valuables are for loading," so that Mormont's dialog would still be grammatically correct.