Revealing mistake: When Queen Elizabeth arrives in disguise, Blackadder welcomes her and is about to open the door to the closet, but you can see the door is being pushed up from the inside, probably by a crew member. (00:16:50)
Visible crew/equipment: After Blackadder has pushed Queen Elizabeth into the closet and sits down at the table, Percy "coughs". When it cuts back to Blackadder, you can see the boom mike above his head. (00:17:00)
Continuity mistake: When Blackadder calls for Baldrick to fetch his incredible strong ale you see Melchett holding his beer down. When it cuts the ale is up at his chest. (00:22:25)

Continuity mistake: There is a knock on the front door, and Blackadder tells Baldrick to 'get the door'. Baldrick returns with it, but the front door on the set, still in place, is still visible in the background of the shot.
Continuity mistake: When Blackadder, Queenie and Nursey are all comforting Melchett, there is a shot from the side view of Melchett, he is holding his head with his left hand. Then there is a shot from behind Melchett, he still has his hand on his head but when the shot returns to the side, Melchett no longer has his hand on his head.
Continuity mistake: There is a knock on the front door, and Blackadder tells Baldrick to 'get the door'. Baldrick returns with it, but the front door on the set, still in place, is still visible in the background of the shot. The fact that Baldrick knows who was at the door indicates that he's got the right one.
Audio problem: When Blackadder explains to Baldric about what he is not allowed to prepare for dinner Blackadder says "And that means no meat." There is a glitch before he says meat, it may be where they stopped recording before the sentence was finished.
Continuity mistake: When Blackadder and Melchett are about to punch the German guards in the groin, Melchett has his hand on a paper. When it cuts his hand is no longer on the paper. (00:23:00)
Continuity mistake: Right at the very end, when everyone is lying dead on the floor, Stephen Fry's eyes are still moving. (00:29:00)

Continuity mistake: At the very end of the episode, when it shows you all the dead bodies, you can see Queenie to the right for a few seconds. The dagger she is holding is pointing upwards. Then there is a close-up of Queenie, who then talks back to you in Prince Ludwig's voice, and the dagger she is holding is now pointing downwards.
Visible crew/equipment: In the shot after Blackadder has read up Baldrick's votes a microphone is visible in the upper right corner. (00:18:15)
Visible crew/equipment: During the conversation between Blackadder and Baldrick, as Baldrick explains what he spent the £400,000 on, we can see the shadow from the boom mike moving on Blackadder's fur coat. (00:28:00)
Revealing mistake: When Baldrick is on the metal spit rotating by the fire, the fire is just a light up board.
Revealing mistake: When Blackadder lifts the huge turnip it looks really light. A turnip that size would weight a fair bit.
Factual error: Dr. Johnson completed his dictionary in 1755, 7 years before the Prince Regent was born (1762). So it's unlikely for him to be asking the Prince for patronage.
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