The robots saying "Eliminate!" is a reference to the Daleks in Doctor Who saying "Exterminate!."
The robot who saves Homer's life by pushing him out of the path of an oncoming truck (and being himself hit as a result) is similar to the self-sacrificing robot in the 100th episode of The Twilight Zone, "I Sing the Body Electric."
When Smithers is throwing books at the robots he says "to servos with love," a reference to the movie To Sir with Love.
The jersey on one robot says "Nomad J25," which may be a reference to the main character in the 1956 novel The Stars My Destination.
Lenny playing the "world's smallest violin" is a possible reference to the SpongeBob SquarePants episode: "Squilliam Returns" or the movie Reservoir Dogs (1992) quote of Mr. Pink.
When Barney becomes a stripper he says that The Full Monty gave him the inspiration.
The summary of the episode is a reference to the Mexican animated film, Top Cat: The Movie, as they both involve robots taking over almost everyone's jobs.
The couch gag of this episode shows a time lapse shot (spanning 1989-2012) of the Simpson family sitting in front of a banner reading "America, Most powerful country in the world." The banner slowly degrades over time as characters from past episodes appear. Things and characters depicted include:
The last time robots worked at the Springfield Power Plant while Homer still worked there was in "Lisa's Wedding." Or rather, this is the first time, and that is the second time, given the idea that that is set in the future.