Three hours at FL100
 

This flight got to 24,000 feet, then squawked 7700 and dropped 14,000 feet in 5 minutes, which I assume was due to a loss of cabin pressure. I was expecting it to land at a nearby airfield, but it proceeded to fly to its destination, arriving about an hour late, and having flown for about three hours at just below 10,000 feet. Is this normal?

Fuel flow will be higher but why not if it was pressurisation only? Especially if you've got enough fuel and the maintenance needed might be available at the destination. During the Cold War all (well most of them) Berlin flights went at around 10k feet through the Berlin air corridors through east Germany due to allied agreements from piston engine days.

I guess I'm imagining that if you have a loss of cabin pressure, you get on the ground as soon as possible to try and work out what is wrong with the aircraft. ¯\_(ツ)_/¯

After the BEA Vanguard crash in 1971 (pressure bulkhead failure) I remember flying up to Edinburgh at 10,000 feet and weaving between clouds as we went.

If you're going from A to B then you only want to go to C if it's really necessary for flight safety. Planes don't require pressurisation at 10,000ft, but they do use a lot more fuel so one of the main considerations is can we continue our not.

Had that years ago on Banff 727 TUL- ORD - passenger window started to emit loud whistling noise, Captain summoned, drop to 10,000ft and slog in all the way.

No, not if you have only lost pressurisation capability, it depends on the situation. It could be that a bleed valve or both packs or an outflow valve have gone unserviceable, but you can fly safely without those, as long as the plane is otherwise healthy.

So there is no automatic need to divert - it's not going to fall out of the sky or explode. This assumes reasonable weather and flying conditions at FL100, and sufficient fuel of course.

Making that call is what the pilots will decide as part of their TDODAR deliberations, along with passenger and crew comfort.

I was taught it was all to do with the Partial pressure of Oxygen at FL100. After all, the air we breathe is only 20% Oxygen anyway.
Sufficient there for the human body to operate then. Above FL130, a different matter.
Even normal pressurised cabin altitudes are FL80 -100.
So only the fuel state/burn at that level is the final deciding factor on whether to continue.

well you don't want a window or door popping out but all in all it seemed to be the logical thing to do - it was damn turbulent tho' at the lower levels in mid summer

Normal, no, but if you're asking if it's doable and safe; then yes.

Squawking 7700 and then continuing for 3 hours is a little odd though, or was it a case of squawking 7700 for the descent only.

If the crew had a pressurisation problem, then descended, decided it wasn't a problem at the lower level, and then continued to destination, I'd expect the latter case.