Elliot's father Edward Alderson was killed by E Corp. In a flashback, Edward decides to reward Elliot for stealing from a jerk rather than punish him. This rather concisely explains why Elliot has chosen his father to be the face of his vigilante anarchist personality.
The shoe store clerk's lecture to Angela is doubly ironic because not only is he lecturing her on E Corp's evil when SHE lost her mother to their actions but the fact is that he's doing his job for her (a member of E Corp) because he needs the money—exactly the excuse he tried to repudiate.
Elliot saying "fuck society" at the start of the series playfully foreshadows his true identity as the founder of fsociety. The "f" in the group's name is simply a shortening of the full swear word, as in "eff society."
The album titles Elliot chooses tend to hold a cryptic significance to the information encrypted within. In Shayla's case, it's The Cure's Disintegration, which contains "Pictures of You", the song that was played when Elliot first met Shayla, and also lent a bitter poignance by Shayla's death, and the fact all Elliot has left of Shayla is whatever information about her he could hack - literally all he has left of Shayla are snapshots - which is what the lyrics of "Pictures of You" deal with.
In one scene between Tyrell and his wife, she's scrubbing a stain off her dress in the kitchen sink while discussing their schemes. Mundane enough activity, but considering what kind of wife Joanna is, it also doubles as a subtle Out, Damned Spot! allusion.
Near the end of Season 2, Angela is given a series of Armor-Piercing Questions by a young girl who looks a bit like her, which later turn out to be courtesy of White Rose as part of her recruitment. Seems weird enough, right? In a flashback in Season 3, we see a young Angela... played by the same girl. What did White Rose do?
With both his mother and father dead and assuming he wasn't adopted by their bodyguard, the Wellick's only child is gonna have a tough life ahead of him.