Deliberate mistake: Edmund's "recollection" of seeing Henry Tudor includes the footage that the audience saw at the beginning; however, Edmund wasn't present when this happened, and thus should not be able to recollect it. Moreover, this scene occurred after Henry had escaped and was in safety, altering the details of the Battle of Bosworth Field. Clearly, the footage was added for the audience's benefit, to be able to link the injured Henry to the introductory scene at the start of the episode.
Plot hole: In 'The Foretelling', it is said that Richard IV reigned for "13 glorious years" with a caption showing 1485-1498. 'The Black Seal' starts on St. Junipers' Day, 1498, but Blackadder spends 12 months locked up with Mad Gerald. So when the Royal Family are finally murdered it is actually 1499.
Visible crew/equipment: After Blackadder has his haircut, the camera zooms in on his foot. He lifts his foot revealing a red tape marker on the floor. (00:21:50)
Continuity mistake: When Blackadder beheads King Richard, Richard's head and helmet change position while lying on the ground. (00:09:00)
Continuity mistake: When McAngus empties his bag on the table and the head falls on it we see the back of the head is turned against the camera. When it cuts to a close up of the head the head is facing in the direction of the previous camera take. When it cuts again the back of the head is turned against the camera. (00:11:25)
Visible crew/equipment: Just after Edmund, Baldrick and Percy get up from sitting by the fire, and before the line "The Black Adder will be King next", the shadow of the boom mike can be seen on Baldrick's hat - it moves upwards quickly so can be hard to spot. (00:06:15)
Visible crew/equipment: When Harry tells Blackadder to be in charge of the welcoming of King Richard's return, as Blackadder turns around and walks against the fireplace saying "12 months of chasing sheep.", if you look closely on the top of the fireplace you should be able to see the shadow of the boom mic moving. It's quite hard to see, but it's there. (00:03:45)
Visible crew/equipment: In the final shot where Percy and Baldrick have entered the room and said their lines, as it fades to black the crew can be heared applauding.
Visible crew/equipment: After King Richard has been crowned, Blackadder, Baldrick and Percy return to their chambers and start cheering. When Blackadder says "We're safe, and I am a prince of the realm" you can see the boom mike move up in the right corner of the screen. (00:16:50)
Visible crew/equipment: When Harry comes to see Blackadder and asks how the entertainment program is going, Harry says that St. Leonards himself was a eunuch. As it cuts to Percy agreeing, you can see the boom mike move right above Baldrick. (00:08:40)
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)
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)
Visible crew/equipment: When Blackadder returns to the castle after rounding the sheep, Prince Harry says "Ah, Edmund." Blackadder then walks behind one side of the wall. The shadow of a boom pole can be seen on the right side of the wall as he does this. (00:02:40)
Continuity mistake: After Blackadder talks to Baldrick and Percy about the plan, Blackadder walks to the window to notice MacAngus getting on a horse to exit the castle. The shot where Blackadder walks over to the window shows only one window above the window Blackadder looks out of and nothing more. A couple of shots later when the camera is in front of Blackadder, two extra windows have appeared from nowhere. There was an iron maiden there which could have blocked the view, but at least six inches of wall are shown between the iron maiden and window, so the window couldn't have been blocked by it. Not to mention the window panes are in a grid of 3x3 from inside, but 4x4 from outside. (00:15:45)
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