In Season 1, episode 9, Game 7 of the 1987 Stanley Cup is seen on TV at the Beeman Family's party. In the Season 1, episode 10, set a few days later, another hockey game is shown on live TV before the cut to breaking news.
When Phillip is dropped off at his hotel, he opens his door with a key. The hotel room next door has a highly visible card reader which was not widely available during the time period.
During the raid on Gregory's apartment the SWAT team can be seen wearing modern tactical gear including PASGT (Kevlar) helmets which, at the time, were just being introduced to the US military and would not have been in use by local SWAT teams yet.
'Grandma' aka Claudia mispronounces the name of Dzerzhinsky street, where the KGB offices in Moscow were situated. As an ethnic Russian, she would know the correct pronunciation and use it automatically.