First of all, I just have to say: I'm really not sure about the title of this episode. World War Two was a rather serious event - it's not that you can't set light-hearted things during that period, but such a flippant title just seems... wrong. Oh well.
Of course, the reason for the title is that this episode, among other things, acts as one of our occasional reminders of why the Doctor can't just stop all the nastier bits of history from happening. This has been done most effectively in another Classically-themed episode, 'The Fires of Pompeii', in which the tragedy of allowing - or causing - thousands of people to die is fully explored, while some way of alleviating the utter horror of the situation is also found. Here, it was just one thread among many and got a bit lost - though the Justice people did note that they don't actually interfere with anybody's timeline, they just torture criminals after they've done their worst. Charming.
We found out in this episode why River became an archaeologist - it seems she thought the study of the physical remains of earlier civilizations would help her to find the Doctor. Well, there's a certain logic to that! (I should perhaps point out, real archaeologists don't take it up in hopes of finding a good man. Although the gender split is fairly even, there are more and more women taking up history and archaeology - if you want men, you want engineering!) She obviously takes her training to heart later, as the older River's attitude and ideas are sometimes reflective of her chosen career, but here she has no idea about history or archaeology, other than having a decent of knowledge of major disasters the Doctor didn't stop. My favourite thing about this episode, as a person who thought the Romans were boring and Latin useless while in school, was the total lack of interest 'Mels' had in history at school, since her preoccupation was with the Doctor, not with history itself (also a really nice way of foreshadowing her identity and her antagonism towards him). Having said that, she did appear to have poisoned him with some kind of intergalactic hemlock, given the way his legs went first. I would ask how come something kept in her lipstick didn't poison her too, but I think that would go against the spirit of the show.
I totally, totally loved the Star Trek vibe that was all over the justice-ship-robot-thingy. Well, Star Trek via Red Dwarf (their raison de'etre is a bit like an especially creepy cross between the Justice zone and the Inquisitor) and Galaxy Quest (pointless corridors above empty spaces). They even look particularly like the brown-suited officers assigned to Temporal Investigations from Deep Space Nine and Voyager. I have to say, when the Justice people saw the TARDIS and said they'd found the greatest war criminal of all, I really thought they meant the Doctor, but apparently the mass genocide of two races is either totally fine by them, or something about the way in which the Doctor 'resolved' the Time War means they're unaware of it/it's not in their timeline. Or something.
I also enjoyed seeing Rory kick ass a little bit in this episode - lest we forget, he is a trained Roman soldier and has two thousand years of guarding a box behind him, so he has his uses in an emergency. I liked seeing the Doctor's old companions in the TARDIS as well, though I would have thought the best, and most guilt-free, choice for a shape and voice would surely be 'Sexy', the human form of the TARDIS herself.