In Three Days of the Condor (1975) starring Robert Redford, a CIA building is hit. Subsequently, a list of the casualties is displayed, the final two names on the list being Martin and Bishop, which is Redford's alias in Sneakers (1992).
'Prof. Len Adleman' is one of the three mathematicians who invented the RSA (he's the "A") cryptosystem, currently the preeminent method of encrypting any form of data in the world. Adleman served as a mathematical consultant on the film, and spent several days constructing the slides Janek displays at the college symposium on "unbreakable codes" (which took Adleman a considerable amount of time to create using primitive early-'90s computer graphics technology). In the end, director Phil Alden Robinson had the slides transposed as oil crayon scribbles, on account of the notion that "that's what a regular mathematician would have done". Adleman later remarked that this was indeed true and what he would have done, and would have saved him days if only he'd known.
In the 1965 thriller "Blindfold", Rock Hudson's kidnappers drive him past a lake with a gaggle of geese nearby. He later thinks this was the sound of the guests at a cocktail party - until he retraces his route and discovers the actual source of the sounds. This idea was borrowed by the producers of "Sneakers" in 1992 when Robert Redford is kidnapped, blindfolded, and also thinks the sound of the geese he passed where people at a cocktail party.
In an article he wrote for Slate in 2012, Stephen Tobolowsky recalled that while shooting on the Universal Studios lot, he saw Robert Redford and James Earl Jones pass unnoticed in front of a tour bus while dozens of tourists instead snapped photos of inanimate attractions such as the bike from E.T. and the shark from Jaws.
While picking through Dr. Brandes' trash, Mother holds up a folded box of "Cap'n Crunch". In the 1970s, "Cap'n Crunch" came with a small whistle in the box. A "phone phreaker" called "Captain Crunch" (John Draper) discovered that this whistle could be used to get free phone calls (one of many components in the practice of "phone phreaking", which digital phone switching-systems has made almost totally obsolete). There is another reference to Draper during the Scrabble game (the word "CRUNCH" is visible upside down before it gets turned into SCRUNCHY). Also, Cosmo tells Martin that, while in prison, he helped some Mafia men to make some "free telephone calls." Whistler is patterned after Joe Engressia, a blind telephone expert born with perfect pitch who was one of the original phone phreakers.
The computer in the room off of Cosmo's office in the PlayTronics building (the one that looks like a circular bench) is actually a Cray Y-MP, a multi-million dollar supercomputer that was one of the worlds fastest computers at the time the film was made.
In 2012, the online magazine Slate published a series of articles about Sneakers commemorating the 20th anniversary of its release. These included a piece by actor Stephen Tobolowsky (Werner Brandes) in which he said, "I can't remember having so much fun on a movie."
James Earl Jones' character, Bernard Abbott, was named after Robert Abbott, a charismatic technical consultant for the film. In addition to being about the same age and complexion as Jones, Bob designed the first time-sharing (multi-user) operating system for the Control Data Corporation CDC-6600, the predecessor of the Cray Y-MP seen in the film. He is also often referred to as the "Father of Information Security" by seasoned veterans of the computing industry.
When Whistler and Mother break into the air traffic control computer, the map displayed is part of the actual airspace above the San Francisco Bay Area. Groups of five letters are airspace fixes and groups of three are airports.
When Liz goes to the Dim Sum bar with Werner Brandes under the assumed name of Doris, there is a group of singers singing the song "Bad, Bad Leroy Brown" in Chinese. In the English version of the song, Leroy Brown gets in trouble over a girl named Doris.
The code spewing on the screen, reflected in Whistler's glasses for effect, as Mother accesses connections in the Black Box is ~12 lines of repeating gibberish except for the entries "mnop=fred/14cb", "ploo", and "123". "[des]" appears, as well as "cap=dw". These cryptic references may be meaningful.
The movie deals with the impact of a factoring breakthrough on encryption, an obvious reference to the RSA algorithm, the most popular public-key encryption algorithm in use today. 'Prof. Len Adleman', one of the co-inventors of the RSA algorithm, provided some technical guidance on the film in exchange for giving his wife a chance to meet lead actor Robert Redford.
Once they have identified Janek's little black box in his office, Mother is fitting Bishop with a hidden microphone and earpiece while in the van. Mother praises the quality of the microphone and observes that it's the same one "that NASA used when they faked the Apollo moon landings. The astronauts broadcast around the world from a soundstage at Norton Air Force Base in San Bernardino, California." The Aerospace Audiovisual Service (AAVS) soundstage at Norton AFB, San Bernardino, CA, is where USAF Captain Phil Alden Robinson, cut his teeth as a Television Producer/Director in the mid 1970s.
The fictional Coolidge Institute located in Palo Alto, CA is a reference to the Hoover Institute on the Stanford Campus in Palo Alto, CA. However, the Hoover Institute is more of a political policy think tank and Stanford's SRI is more similar in its nature.
The trivia item below may give away important plot points.
The security guard at the beginning of the film (after the flashback) is watching "Touch of Evil." In the brief scene shown on screen, Charlton Heston says, "I just looked in that box...there was nothing there." This is a very subtle giveaway/reference to how the finale plays out on the Playtronics roof when Bishop hands the box over to Cosmo.