Then, after all the information had been filled in and I thought I was booking the flights, it said something of the form `Error. Your purchase cannot be completed at this time. One or more of your flight(s) is not available.' Neither of the two navigation options was useful (`cancel and go to itinerary', which just takes me back to the page showing the flights I had chosen, where I can attempt to rebook the same flights with a similar lack of success, or `cancel and go to referring page', where I can re-type my card details, press `book this flight' and be told that one or more of my flights is not available). And the thing is, you apparently don't get to find out whether your flight is available until after you've pressed the button to make an irrevocable booking, and even then it doesn't bother telling you which flight was unavailable.
Tried it again with different flights - same result. Tried again with the original flights - no dice. And of course you have to go through the whole selecting passenger and then entering card details rigmarole each time in order to be told it can't be done. Meanwhile, the apparently unavailable flights still continue to show up when you search for flights.
Expedia also allows you to reserve a flight you've just found until midnight the next day (though it still requires you to type in a credit card number for some reason). I tried that, and it said something of the form `Your request cannot be completed at this time.' Very useful.
I rang up customer support, to be told `oh yes, that means your flight isn't available and you'll have to choose different flights. Or try again in about an hour in case the airline has supplied some more seats.'
On a slightly different note, the booking form offers you the option to pay by Switch if you are booking flights and a car, but only credit cards are listed if you are just booking flights. Since 
bopeepsheep found a cheaper car on Airline Network we switched to just trying to book the flights and suddenly I couldn't type in my Switch card number any more.
Luckily, my new credit card arrived this morning.
In any case, it appears that Stuttgart is pretty much unavailable, so I've booked to Frankfurt instead and we'll just have a 2.5 hour drive when we get there (which might be a nice way to see some of Germany anyway). Fortunately it didn't give me any of the error messages at all (and it's a few quid cheaper), though it was still a big faff getting all the details into the booking form.
