General Melchicus claims Rome is attacked by barbarians and therefore pulling all the troops back from Brittannia. This implies it is 406 AD. However, the Roman legionaries clearly wear early imperial outfits. 5th century Roman soldiers looked nothing alike.
The Roman Age characters talk in English. Although this might be for audience reasons, general Melchicus compliments them literally 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 Anglosaxons.
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 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.
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.