Julia had two elder sons that died a few years after her banishment. Historically, it was Lucius who died first of mysterious causes of illness and then Gaius who died in a campaign after being wounded. In "I, Claudius" however, it is Gaius who died first of the mysterious causes *before* Julia's banishment and Lucius is the one who dies in the "accident".
Augustus thanks the poet Horace for his performance. Roman soldiers enter to inform Augustus of the slaughter his troops faced at the Teutoburg Forest. Horace died in 8 B.C. and the incident in the forest occurred in 9 A.D.
In "I, Claudius" Tiberius is married to Vipsania at the same
time that Julia is married to Marcellus. Historically, he didn't marry Vipsania till 19 BC, by which time Marcellus had been dead for four years and Julia has been married to her second husband Marcus Agrippa for two years, with one child by him and pregnant with a second.
Augustus remarried a few months after Julia was born. Julia mentions that Livia had been married to her father for twenty years. Historically, Julia would have only been fourteen at the time she said this in the episode.
It has been assumed by many that the reason some of the audio is at too low a level on the DVD is because of some faulty remastering. This is not the case. It is because some of the microphone placement on set during the making of the series was not as polished as it could have been, or as it might be now, and this shows up more clearly on the DVD because of higher fidelity. At certain moments, an actor or actress may be in the rear of the set and his/ her voice is not picked up clearly; then, as the actor advances, the voice becomes louder.