Although I agree that the later series are better than the first, I must say that it was the episode "The Archbishop" that got me hooked. The two lines (I know these aren't exact), "I hope that something slightly unpleasant happens to you, like an onion falling on your head," followed by, "May you be turned orange in hue, and may your head fall off at an awkward moment," had me laughing for a good hour.
Some significant changes were made between the first and later series. Most important, I think, are the changes to Edmund Blackadder himself. Rowan Atkinson stopped using that high voice and made fewer silly faces, and the character himself became smarter and more sarcastic. Baldrick got stupid, and honestly I can take him either way (though I think his stupidity was excessive in parts of the third series, particularly Ink and Incapability). Percy did not really change; he was still an airheaded fop.
In Blackadder the Third, we lost Percy and got George instead, who was similar in his stupidity but somehow funnier about it. Then in Blackadder Goes Forth, Geroge stayed, but Tim McInnerny returned as a new character, Kevin Darling. Darling was very different from Percy; instead of the brainless yet loyal fop, he was quite cunning and semed to enjoy watching others suffer (particularly Edmund).
Flashheart (Lord in II and Squadron Commander Lord in Goes Forth) is also worthy of note. I'm still trying to figure out why I didn't like him in "Bells" and yet "Private Plane" is one of my favorite episodes ever. It could just be that the character worked better when he got a whole episode, instead of just showing up as a Deus ex machina to whisk away Edmund's bride. It could be that the WWI pilot's uniform suited him better than Elizabethan garb. Maybe he just got better lines ("Hey girls, look at my machinery!"). I also like the fact that Edmund didn't like him; I think it made for a more interesting dynamic.
Oh yes: Black Adder's Christmas Carol. At the beginning, Edmund is the opposite of his usual self: so generous he ends up with nothing, and nice to everyone. Then he is visited by the Christmas Ghost (Robbie Coltrane, and I'm quite sure whoever suggested him for Hagrid has seen this), who got the wrong house while out trying to convert the misers. He tries to praise Edmund's generosity but mentions how rotten his ancestors were, so Edmund wants to see some examples. Unfortunately, the ghost is limited to showing Christmas scenes, and it seems Edmund always won out then. The icing on the cake is the future scenes, in which the evil Edmund becomes King of the Universe or something, but the good Edmund is Baldrick's slave. So the current Edmund decides to be evil, and in fact does suffer for it, because Queen Victoria intended to give him a huge reward for being so generous, but he slammed the door in her face.