As the story develops in 1981, the book "Personhood" by Leo Buscaglia (that we see advertised on a TV set during a dialogue between Stan Beeman and his wife) was first published in 1986.
When Gaad is talking to Beeman he says it's been a couple of months since the events of season one, which ended in the spring of 1981. Yet the movie The French Lieutenant's Woman is featured, and it wasn't released until the fall of 1981.
The newspaper Emmett Conners places next to Philip shows two stories; one announcing the Delorean Car Company in receivership (first reported 20 February 1982, the other, the conviction of William Bonin (which occurred 6 January 1982) both newsworthy events occurred weeks apart from each other, and would not have appeared in print on the same date.
As Philip leaves the Afghani restaurant in his first scene, and is headed to his car, a modern slim line HVAC unit on the roof can be spotted.
As Stan leaves the Afghan restaurant, the flag of the modern Islamic Republic of Afghanistan (2002-present) is painted on the door, not the flag of the Republic of Afghanistan.
In late 1981, Sandra Beeman is shown watching what she calls a pledge drive on PBS. The Reagan administration's defunding of public broadcasting, which made public donations necessary, did not take effect until the fall of 1982. In 1981, there were no PBS or NPR pledge drives.
For an FBI agent, Beeman is rather cavalier about lending out pirated video tapes.