The Witchsmeller Pursuivant - S1-E5
Revealing mistake: The edges of Blackadder's bald cap are visible next to his right ear when he is visited by the queen and princess. (00:24:45)
Revealing mistake: At the very end of the episode, right after Edmund drinks the wine, the camera switches to a close-up. Watch the very animated 'dead' extra right behind Edmund who seems to be unsure whether the scene is in the bag yet or not. (00:29:25)
Answer: The closest we ever get to knowing his first name is in series 3, when he claims it's "Sod Off". Blackadder asks him in series 3 where this came from, and he replies "Well, when I was a kid, living in the gutter, I'd go up to the other kids and say 'Hello, I'm Baldrick'. And they'd say, 'Yes, we know. Sod off, Baldrick.'" The S in this series is likely a reference to that, but it's not addressed, and given this Baldrick is clearly different from the series 3 Baldrick, we can't draw a direct link.
Shay