When Margo Madison puts the record on the player you can see how warped it is, not an issue, but when she then goes to put the needle down and listens to the LP you can see the arm isn't moving, when in reality if it was playing the arm would be going up and down with the warp of the record.
Molly's guide dog Ollie is shown wearing a harness at all times, even when lying down resting in Molly's office. In reality whenever their owner doesn't expect to need their guide dog's assistance for a period of time (such as when sitting at their desk working) they always remove the harness. As part of their training, a guide dog knows that it is 'on duty' and working whilst wearing the harness. When the harness is removed the dog then knows it can relax.
In the opening montage there is a 1986 newspaper with the headline "Red Tide", stating that Mexico became a communist after Arnoldo Martinez Verdugo, from the Mexican Communist Party (PCM), won the elections. While both Verdugo and the PCM were real, his party dissolved in 1981. Even for an alternate 1980's this scenario is very unlikely as Mexico was quite famously a single one party regime, and while opposition technically existed, elections were rigged by the ruling party. In fact, the country did not have a truly democratic presidential election until 2000.
In the opening montage, the October 13, 1984 newspaper article concerning the murder of the British Prime Minister Margaret Thatcher by the IRA notes that the Brighton Hotel bombing was condemned by the Irish President Eamon de Valera. In reality, de Valera served as President of Ireland from 1959 to 1973 and died in 1975. The series' alternate history is unlikely to have extended either his presidency or his life.
The slightest friction in the bearings system would cause the 'non-rotating' part of Polaris Hotel, the hub and solar panels, to be pulled by the thruster-driven habitat ring. It would require counter thrusters to hold that section static relative to Earth.
Polaris Hotel has four 'spokes' connecting hub to habitat ring. The thrusters are mounted at the end of spokes, beyond the habitat ring.
At 12:12, 32:23, and 39:00 views of Polaris show two spokes and each time one of those main thrusters is facing against the rotation.
At 56:05 all four spokes can be seen and two thrusters are counter rotation.