Corrected entry: In the episode "Beer", set in the 1560s, the "Happy Birthday" song is sung by several characters. This song was not written until 1893 by two American school teachers, copyrighted in 1935. Neither is the song in the public domain. It still earns significant fees to the copyright holders each time it is recorded for sale, i.e. in a movie or on television. In most of the episodes, the various historical inaccuracies are intentional. This one, though, appears to have been an accident, a genuine mistake on the part of the writers. It should be noted that unintentional historical errors are very rare in Blackadder, "unintentional" being the key word.
Corrected entry: I know Percy's not that bright, but he adds "Cardinal Wolsey" to the list of party guests. Given that Wolsey died in 1530, and Queen Elizabeth ruled from 1558 onwards (she wasn't even born until 1533), he must have been dead for at least 28 years by this point (even in the Blackadder world of history). Obviously it's done for the joke, but it's still wrong.
Correction: A self-correcting mistake. Percy is an idiot. He said the first name that came into his head without stopping to realise Wolsey is dead.
Correction: There is no way this mistake could have been overlooked in the production process. For starters the producers would have had to pay the royalties. This is entirely a deliberate gag by the writers.