As you know I do a lot of miles on my trusty fleet of bicycles and I regularly get punctures, especially when the road is wet. There is something about wet rubber which means it punctures more easy, not 100% sure why.
I use the green slime on most of my bikes, it works pretty well although my aim is to reduce rolling resistance
and weight in order to increase my average speed. It's only a few percent difference but over a hundred or so miles it makes a big difference, especially on hilly competitions.
That said, it wont protect against the b@astard of all punctures that is slate clippings or it's slightly less annoying brother "the rim killer stone" (which you cant see until it's too late) For that I always carry a couple of inner tubes with a spare tyre and/or a section of old tyre cut out for those bigger holes which you place inside the damaged area to stop the new tube blowing out of the hole. This saved my arse once in the Alps when I was 30 miles from my hotel, with no support, no phone signal and on a sunday when the Taxis wouldn't even answer their phones let alone work. When riding the carbon rims I use tubular tyres so I can get about 160-180 PSI in the tyres, they are rated to 200 but then you have to allow for rolling and braking heat. When they blow out you rather know about it!

Back the OPs post, if they fitted the new tube without removing the old thorns then that is pretty negligent. If someone had been riding it afterward and came off because of the new puncture then I guess it would fall under the same legal responsibilities as if a mechanic failed to fix a safety related item properly and it failed shortly afterward.
In your favour, the managers at Halfords are generally pretty generous when they get it wrong. I once had the wrong bottom bracket delivered to a store which I needed to take out to france for my bike over there. They would not be able to get another one in before I left so he get the best quality model he had in the shop that would fit and gave it to me.