The Marathon - S4-E3
Plot hole: Jason cheated in three different ways in order to beat Aurelius in The Marathon, and admitted it. So the bet that they made between them is null and void. But the last shot shows them living up to the terms, which includes Aurelius starting to eat his own shit (literally), so revolted that he's trembling. Apparently the writers really really wanted to include coprophagy. But who would eat faeces for a bet, if you can simply avoid it by reminding your opponent that he cheated? Or even better, many would say that cheating means losing automatically, so he's the one who should be eating his own shit.
The Banquet - S5-E3
Factual error: The library contains books as we know them, with a spine. But Roman libraries had scrolls.
The Banquet - S5-E3
Factual error: During The Banquet, everyone is seated at the dinner table. But Romans famously ate reclining. They should have lain down to eat.