The Case of the Wayward Wife - S3-E13
Factual error: May buys a book for 4.95. Give the clerk a $10 bill but the register shows change of $5.15.
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.