Davos' joke to Gendry about him thinking he might be "still rowing" is a nod to a known joke among the fans of the show that started after Gendry (Joe Dempsie) rowed away from Dragonstone during the season 3 finale Mhysa (2013). After The Children (2014) (the season 4 finale) was aired, people started to wonder about where Gendry went, until Dempsie himself shared a tweet saying "Still rowing". Since then, the fans and even crew members of the show often joked about Gendry's long absence from the show, being explained by him that he was somewhere on his boat all this time, still rowing.
Gendry's war hammer is emblazoned with the head of a stag, the symbol of his late father Robert Baratheon's house. It seems fitting, considering Gendry is the last person alive with Baratheon blood. Moreover, the war hammer was also Gendry's father weapon of choice in the novels, with which he famously slayed Rhaegar Targaryen during his rebellion against the Mad King. Note, however, that it is a golden stag on a black background, whereas the Baratheon sigil is a black stag on a golden background; in the novels, bastards who have not been legitimized cannot use their parents' sigil unless the color scheme is reversed. Although some claim that the hammer appears to be made of dragonglass, this has never been confirmed; since it was made before Gendry traveled to Dragonstone, it is highly unlikely that he was able to obtain the material, or knew that it would be an effective weapon against the wights (which isn't common knowledge).
This episode marks the return of Gendry, who hasn't been seen since Mhysa (2013); he turns up in the same shop in the Street of Steel as where he was first introduced in Cripples, Bastards, and Broken Things (2011). In the 'Inside the Episode' video, the showrunners stated that due to uncertainty about which plotlines from the novels they could adapt, they had to tell the actors that characters such as Yara Greyjoy and Edmure Tully might not be coming back; however, Gendry had always been in their outlines for future seasons, so there was never any doubt that Joe Dempsie would be asked back.
The episode title refers to Eastwatch-by-the-Sea, the easternmost castle and port on the Wall where it ends at the Shivering Sea. Together with Castle Black in the middle of the Wall and the Shadow Tower on its western end, Eastwatch is only one of three Night's Watch castles that are still manned, and this episode marks the first appearance of it in the series. It hasn't been seen in the novels yet, and is described to have docks, but possibly only for smaller ships.
The first time Tyrion and Jaime meet since The Children (2014). Tyrion takes the risk of being recognized by the Goldcloaks, knowing that secretly contacting Jaime is the only way to persuade Cersei (although Cersei finds out anyway, probably via Qyburn's network of "little birds"). In 'A Dance with Dragons', the fifth novel, Tyrion flees to the Free Cities of Essos, where he is advised to hide his identity; he doesn't see the point, and sarcastically mentions that he'll claim to be another dwarf with a horrific and distinctive facial injury if he gets caught.