The Hoodlum - S4-E1
Factual error: Diamond's car phone, quite a rarity in the 1950s, attracts a lot of attention. But the car should have a huge antenna attached to make the gadget work (it doesn't), and Diamond would not be getting direct calls - they'd have to go through a mobile operator first.
Stage West - S1-E6
Factual error: In the background, in the scene when Simmons is talking to the stage driver, you can see cars driving by on a road in the background. (00:12:06)