And you ask why I love Donna.
I love how the Doctor is just like “I’d listen to her if I were you…”
It’s a delightful scene, but there’s one thing wrong with it: he shouldn’t be saluting her, or indeed anybody, because he hasn’t got his hat on.
In British military usage (and UNIT is essentially British in all important respects: always has been), salutes are properly rendered only by servicefolk who have their hats on. This is because the salute is a symbolic removal of your hat.
The way to make this work would have been: officer reacts, gets his hat, puts it on, salutes: then takes his hat off and picks up where they left off. (Would’ve been even funnier if he had to do it twice.)
And yes, this means that John Watson shouldn’t have done it in “The Hounds of Baskerville,” either. John ought to have got even more fun out of that pulling-rank moment because he could have ordered that young officer around and not had to return his salute, because John was neither in uniform nor wearing a hat. (The ex-RAF guy sitting next to me, and to whom I am married, just spent some while describing the delicious torment one could inflict on those in uniform when you weren’t in uniform and nonetheless outranked them.)
What does all this mean? That Steven Moffat needs better military vetting on his series’ screenplays. That’s all.
Both of those are hilarious scenarios and this is why nitpicking and good consulting about (well, any) professional details can actually lead to better writing; they’re not things that drag scripts or stories down.