Malory: What year do you think this is? Archer: I, uh— yeah, exactly. Good question.
Archer, according to Word Of God, is deliberately an Anachronism Stew because they wanted a Mad Men feel, but also wanted cell phones so characters wouldn't have to find a payphone to call someone, and so contains cars from the '50s to the '70s, computers from the '80s that are capable of internet access, reel-to-reel mainframes and dot-matrix printers, décor, clothing and hairstyles from the '60s and modern cell phones, pop culture references and racial and gender treatment.
Police cars are 1963 Ford Galaxies but have the modern "blue on white" livery NYPD has used since the early '80s, license plates are the current (April 2010-on) "Empire Gold" pattern — black band and orange NEW YORK at the top, orange background and black letters in the middle and EMPIRE STATE at the bottom.
This mention of a comedian:
Cyril: Shouldn't I learn Karate or something?
Archer: Karate?? The Dane Cook of martial arts?!
Cadillacs are all 1967 models, while Lincoln limos are 1966 Continentals, but also appear with 1974 Mark IV Continentals.
The Soviet Union collapsed and Germany is reunited (at least, as of the map seen in the control room in season two) but Russia is still run by the Communist Party, meaning the show occurs in an Alternate History or Multiple Choice Pastnote Germany reunited in October 1990 but the USSR became a multi-party state ruled by a President in March of that year, with satellite republics declaring independence from March 1990 to December 1991; the Soviet Union announced its own dissolution on Christmas day 1991. The Lubyanka◊ has its symmetrical post-1983 façade◊ and is still KGB headquarters, and Leningrad is referred to as St Petersburg.
Archer is stuck at the Casino de Montréal, which was built as the French and Quebéc Pavillions for Expo 67, and opened as the casino in 1993.
Woodhouse and his squadron mates are World War One veterans, which, today, would make them at least 115 - not impossible, but extremely unlikely - but seem to be in their 70s or 80s, while Malory is a World War II veteran but is in her 50s or 60s.
In Real Life the last veteran of World War I passed away in February of 2012. (Most of the characters' backstories and ages also contradict an Alternate History contemporary setting, but Woodhouse is perhaps the strongest argument for the setting still being earlier than The Nineties, despite all the modern references).
Burt Reynolds appears with silver hair, like he has in the present day.
Archer's age in the pilot is given as 35, and his birth in Morocco during an OSS operation just before World War II indicates 1938 to 1940, making the pilot 1973-75, and Archer is shown to be five-ish when Malory returns from the war. However, he's also shown as being around ten while being read a telegram from Malory about Operation Ajax, conducted in 1953, and is stated to be six when Malory was part of the Guatamalan coup d'etat in 1954, changing his birthdate to 1948. He's also shown as a teenager in a setting that can't be any later than the late 1940s, which could push his birthdate as far back as 1927. This leads into Multiple Choice Past, especially considering that in some episodes, Mallory is shown raising Wee Baby Seamus in the same way she raised Archer, and in other episodes, Malory was completely absent in Archer's life from when he was a few days old to around five.
Zima was marketed in the US from 1993 to 2008.
Flashbacks to Lana's college years have a 60's-70's hippie aesthetic, complete with Lana sporting bell bottom jeans and a huge afro.
In one episode, Archer references the character Wolverine and asks if anyone else at ISIS reads X-Men. X-Men was first published in 1963, while Wolverine didn't debut until 1974.
In a later episode, Pam and Archer have a conversation where they mention the Marvel Comics superheroes Cypher and Gambit. The two characters were created in 1984 and 1990, respectively.
In the Season 4 premier, Archer mentions the old Shazam live-action show, which ran from 1974-1977. He also mentions She-Hulk, who debuted in 1980.
The president of Turkmenistan is explicitly identified as the current leader Gurbanguly Berdymukhammedov, but with several of the Bunny-Ears Lawyer traits of his predecessor, Saparmurat Niyazov, who served as head of state from 1985-2006.
The moon landing has already happened and NASA is staffed primarily with ex-Nazis. The Moon landing happened in July 1969, while the Nazis recruited by the US government post-World War II retired or died in the 1970s-1990s.
Archer is enemies with Shining Path, which was founded in 1980, and the Stasi, which existed from 1950 to 1990.
Bearer-bonds are still issued. Because of their ease of use for money laundering (they have no registered owner and therefore no paper trail), bearer bonds stopped being issued in 1980.
Archer mentions having seen Top Gun as a young man. The film was released in 1986.
Rap music is already around and popular, as evidenced by the Running Gag featuring a song called "Mulatto Butt" and several references in "Midnight Ron".
Krieger is explicitly stated to be a fan of the band Rush, who didn't form until 1968.
In "Drift Problem", a 2002 Citrëon Jumper is in the background when Cheryl drives Malory to the drift race.
The RCMP officers in "The Limited" ask the passengers to have their passports ready, and Sterling is stranded in Montréal because he burnt his passport in "Midnight Ron". Passport checks on the Canada-US border were required starting in 2008. The RCMP also use Webley Mk. IV revolvers in .38 S&W. The RCMP long ago switched to Sig Sauer 220 and Smith and Wesson 5946 semiautomatic pistols.
"Space Race" has a multinational crew on a space station; the International Space Station, which launched in 1998, is the only space station to date with multinational crews. The space station itself feels like something out of a science fiction novel and is more advanced than anything currently in orbit.
While the ISIS staff can be decidedly offensive at times, chances are their behavior towards Lana would be a lot different in the actual 50's or 60's.
Ray is licensed to perform marriages but cannot get married himself. New York legalized same-sex marriage in mid-2011.
North Korea can't make its own weapons-grade uranium; enrichment technology was introduced in that country in the mid 90s.
The Soviet soldiers in "White Nights" use (actual) AK-47s, with milled receivers. The AK-47 was replaced by the AKM, which has a cheaper stamped receiver around 1959, which was in turn replaced by the 5.45x39mm AK-74 in 1974.
The KGB, which disbanded in 1991, is still around and serves as Russia's primary intelligence service.
Both "The Limited" and "Midnight Ron" show the current Canadian Maple Leaf flag, which replaced the Canadian Red Ensign in 1965.
In "The Papal Chase," the Pope is Italian, this would place the episode sometime between the death of Dutch-born Pope Adrian VI in 1523 and the death of John Paul I in 1978 (given the Pope's role and appearance in the episode, this does leave the possibility of an Alternate History where either John Paul II, Benedict XVI or even Francis' place is taken by an Italian counterpart, although by the time Francis assumed the Papacy -which was also shortly before the episode aired-, there had been no surviving World War I veterans for over a year).
In "Midnight Ron," the Russian tricolor flag can be seen, which contradicts the repeated references to the Soviet Union still existing and general sense of a Cold War setting, as well as multiple appearances of the Soviet hammer and sickle flag, but is consistent with the wall maps seen elsewhere in the series showing current international boundaries.
In "Once Bitten," Malory makes a reference to the Soviet T-72 main battle tank, which entered production in 1970, in a plotline in which Turkmenistan and Russia are separate countries, which implies a post-1991 setting.