Obviously they might be confused by the music and set changes and other quirks of modern cinema, but the plot and humour are intentionally patterned after Roman comedy, especially Plautus's Miles Gloriosus. It's intentionally extremely derivative, which I especially appreciate, since Plautus's own comedy was itself intentionally thoroughly derivative of Greek New Comedy. You can see the classic stock characters of Roman comedy (the lying slave, the young hero in love, the lustful older man, the immoral pimp, the beautiful young courtesan who serves the plot almost entirely as a trophy, the braggart soldier, and many others) which, in Plautine style, show almost none of the subtle, multi-dimensional treatment that starts to creep in with Greek New Comedy under Menander, but instead revel in their simplistic roles; the humour that, again, is far from intellectual, but relies on farcical vaudevillian slapstick and perfect comic timing; the plot, with a plan to acquire the beautiful woman for the young hero that spirals out of control but somehow all ends up well for (almost) everyone, closing to applause and a solution that isn't necessarily morally "right" but is certainly satisfactory to the audience -- it looks most like a Plautus play, with a single simple but hilarious plot strand, but the introduction of Erronius at the end and the reveal [spoiler alert?] that two of the characters are his children kidnapped long ago by pirates gives it a bit of a feel of Terence, the other prominent Roman comedian.

The fact that the modern play/movie is a musical is a subtle nod to Plautus as well, since Roman comedy would have been accompanied by music and clearly involved singing and dancing, although with essentially no stage direction and our highly limited understanding of ancient music, it would certainly have looked very different from the modern version, which is why I mention it above. Lastly (and I rather strongly suspect that I'm reading something unintended into this, but I don't see why that's a problem), I love the subtlety that the modern musical is set in Ancient Rome, which allows the audience to enjoy the foibles and satire of society and humanity in general, but with an archaizing effect that provides a nice, comfortable distance that lets you sit back and enjoy the slapstick (as opposed to the much more aggressive, in-your-face satire of, say, Aristophanes, or half of the shows on my DVR) -- which runs in perfect parallel to the extant Roman comedies, which are all "fabula palliata," set in Greek towns with Greek characters, to precisely the same effect. In other words, we can enjoy the musical with some detachment because even though they speak English, these are Roman characters living in Rome with, for the most part, Roman names (a few, like the slave Pseudolus, have Greek names precisely because they are non-Roman slaves), and an ancient Roman audience had precisely the same effect because even though they're watching in Latin, they're watching Greek characters with silly Greek names (like Pyrgopolynices, the braggart soldier from the Miles Gloriosus) in a Greek town.