Goofs

When the Scots are running towards Hadrian's wall, Blackadder steals the Centurion's helmet. However in next shot looking towards the wall, you can see the helmet's plumage which mean's it's still there.

Blackadder's Roman ancestor is supposed to be a centurion. However, a centurion would have the crest on his helmet from left to right, not from back to front.

The Roman Age characters talk in English. Although this might be for audience reasons, General Melchicus compliments them on practicing their English. The English language did not exist during the Roman Age. The Ancient Britons spoke Celtic languages, while the lingual ancestors of English arrived with the Anglo-Saxons. However, the Romans had been referring to the inhabitants of the south of Britannia as 'Angli' (roughly 'English') and their country as 'Anglia' ('England') since the 1st century A.D. and this appear to be in the 5th century. (The true Angles had been in Britain for a long time by this point.) It is not unreasonable for a Roman to refer to their language as English, even if it is not Modern English.

When Baldrick and Blackadder arrive at Hadrian's wall it is clearly the modern-day ruins of it, leading Blackadder's Roman ancestor to claim that Hadrian built a 3 foot high wall. During the Roman Age, the wall was a much larger structure.

When Blackadder runs into Shakespeare after his visit with Elizabeth I, he picks up a copy of "Macbeth". "Macbeth" was written during the time of James I.

When Blackadder exits the time machine in the Elizabethan era, the wall lights in the basement are electric.

General Melchicus claims Rome is attacked by barbarians and therefore pulling all the troops back from Britannia. This implies it is 406 AD. However, the Roman legionaries clearly wear early imperial outfits. 5th century Roman soldiers looked nothing like this.

Georgius is called a consul. This would make him one of the highest ranking magistrates in the Roman empire. However, General Melchicus does not address him as a superior.

When Blackadder walks down the stairs showing Leonardo Da Vinci's sketchbook, we hear him talking about it, but his lips don't move.

Just after Blackadder waves to his dinner guests and enters the time machine for the first time, you can see a blonde crew member wearing a red shirt pushing up the end of the drawbridge-like door to close it as Baldrick is climbing up through the trap door inside.