I also saw that episode today. The title is "The Shooting Board" as Friday exchanges shots with a miscreant who dies a short time later, causing Friday to have to submit to an internal investigation.
They definitely said it was a S&W .38. I heard the serial number but was too slow to get it all. I know it ended in 806. Must be they didn't think they needed to xx the last two digits.
The date on the show was MCMLXVII (1967). You would assume that a veteran detective like Friday had been carrying the same revolver for years, so my guess would be it should date to the late '50s or early '60s.