Accidental Innuendo: In spades, especially if you're learning Latin and tend to make mistakes translating it, many lines can come out having a completely different meaning to what they are meant to. Even some of the properly translated lines tend towards this.
Beam Me Up, Scotty!: "Caecilius est in horto." In the very earliest stories, Caecilius est in tablino and Clemens est in horto.
Crowning Moment of Awesome: Clemens befriends a cat that lives in the Temple of Isis in Alexandria. Said cat attacks the head of the local mafia.
Ensemble Darkhorse: Grumio. The drunk, dishonest, ladies' man of a cook who went as far as impersonating a Roman citizen. The course is used in a lot of high schools.
Ho Yay: In the second book, Clemens works at a glass shop under the employment of Eutychus. Eutychus is very easily angered by pretty much everything, yet consistently describes Clemens as "mi dulcissime" ("my very good friend!'; literally "my very sweet friend!") and greets him amicissime (in a very friendly way). The UST gets better from there.
Postscript Season: So the writers end the first book with the explosion of Vesuvius and everybody dies, or so we think. Caecilius the main character dies onscreen. It doesn't exactly give the impression there was going to be another book. Then in Book 2 we discover his son miraculously survives and the action is shifted elsewhere. Also, Book IV had a lot of filler arcs, don't you think? Who cares about Those Two Guys at Bath and random weddings? Get back to Salvius and his evil!
Tear Jerker: Cerberus the dog standing guard beside Caecilius' corpse while Vesuvius erupts and buries Pompeii.